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{"id": "atom-0000", "stage": "atomic", "k": 1, "integrand": "-5*x**8", "integrand_latex": "- 5 x^{8}", "integrand_latex_integral": "\\int - 5 x^{8} \\, dx", "reference_antiderivative": "-5*x**9/9", "category": "polynomial", "variable": "x"}
{"id": "atom-0001", "stage": "atomic", "k": 1, "integrand": "-2/x**11", "integrand_latex": "- \\frac{2}{x^{11}}", "integrand_latex_integral": "\\int - \\frac{2}{x^{11}} \\, dx", "reference_antiderivative": "1/(5*x**10)", "category": "polynomial", "variable": "x"}
{"id": "atom-0002", "stage": "atomic", "k": 1, "integrand": "5*x**8", "integrand_latex": "5 x^{8}", "integrand_latex_integral": "\\int 5 x^{8} \\, dx", "reference_antiderivative": "5*x**9/9", "category": "polynomial", "variable": "x"}
{"id": "atom-0003", "stage": "atomic", "k": 1, "integrand": "-4*x**3", "integrand_latex": "- 4 x^{3}", "integrand_latex_integral": "\\int - 4 x^{3} \\, dx", "reference_antiderivative": "-x**4", "category": "polynomial", "variable": "x"}
{"id": "atom-0004", "stage": "atomic", "k": 1, "integrand": "-5/x**13", "integrand_latex": "- \\frac{5}{x^{13}}", "integrand_latex_integral": "\\int - \\frac{5}{x^{13}} \\, dx", "reference_antiderivative": "5/(12*x**12)", "category": "polynomial", "variable": "x"}
{"id": "atom-0005", "stage": "atomic", "k": 1, "integrand": "3*x**4", "integrand_latex": "3 x^{4}", "integrand_latex_integral": "\\int 3 x^{4} \\, dx", "reference_antiderivative": "3*x**5/5", "category": "polynomial", "variable": "x"}
{"id": "atom-0006", "stage": "atomic", "k": 1, "integrand": "-2*x**7", "integrand_latex": "- 2 x^{7}", "integrand_latex_integral": "\\int - 2 x^{7} \\, dx", "reference_antiderivative": "-x**8/4", "category": "polynomial", "variable": "x"}
{"id": "atom-0007", "stage": "atomic", "k": 1, "integrand": "3/x**2", "integrand_latex": "\\frac{3}{x^{2}}", "integrand_latex_integral": "\\int \\frac{3}{x^{2}} \\, dx", "reference_antiderivative": "-3/x", "category": "polynomial", "variable": "x"}
{"id": "atom-0008", "stage": "atomic", "k": 1, "integrand": "4/x**7", "integrand_latex": "\\frac{4}{x^{7}}", "integrand_latex_integral": "\\int \\frac{4}{x^{7}} \\, dx", "reference_antiderivative": "-2/(3*x**6)", "category": "polynomial", "variable": "x"}
{"id": "atom-0009", "stage": "atomic", "k": 1, "integrand": "-5*x**9", "integrand_latex": "- 5 x^{9}", "integrand_latex_integral": "\\int - 5 x^{9} \\, dx", "reference_antiderivative": "-x**10/2", "category": "polynomial", "variable": "x"}
{"id": "atom-0010", "stage": "atomic", "k": 1, "integrand": "x**(-5)", "integrand_latex": "\\frac{1}{x^{5}}", "integrand_latex_integral": "\\int \\frac{1}{x^{5}} \\, dx", "reference_antiderivative": "-1/(4*x**4)", "category": "polynomial", "variable": "x"}
{"id": "atom-0011", "stage": "atomic", "k": 1, "integrand": "-2*x**15", "integrand_latex": "- 2 x^{15}", "integrand_latex_integral": "\\int - 2 x^{15} \\, dx", "reference_antiderivative": "-x**16/8", "category": "polynomial", "variable": "x"}
{"id": "atom-0012", "stage": "atomic", "k": 1, "integrand": "-4/x**13", "integrand_latex": "- \\frac{4}{x^{13}}", "integrand_latex_integral": "\\int - \\frac{4}{x^{13}} \\, dx", "reference_antiderivative": "1/(3*x**12)", "category": "polynomial", "variable": "x"}
{"id": "atom-0013", "stage": "atomic", "k": 1, "integrand": "2*x**2", "integrand_latex": "2 x^{2}", "integrand_latex_integral": "\\int 2 x^{2} \\, dx", "reference_antiderivative": "2*x**3/3", "category": "polynomial", "variable": "x"}
{"id": "atom-0014", "stage": "atomic", "k": 1, "integrand": "x**(-13)", "integrand_latex": "\\frac{1}{x^{13}}", "integrand_latex_integral": "\\int \\frac{1}{x^{13}} \\, dx", "reference_antiderivative": "-1/(12*x**12)", "category": "polynomial", "variable": "x"}
{"id": "atom-0015", "stage": "atomic", "k": 1, "integrand": "5*x**4", "integrand_latex": "5 x^{4}", "integrand_latex_integral": "\\int 5 x^{4} \\, dx", "reference_antiderivative": "x**5", "category": "polynomial", "variable": "x"}
{"id": "atom-0016", "stage": "atomic", "k": 1, "integrand": "4/x**9", "integrand_latex": "\\frac{4}{x^{9}}", "integrand_latex_integral": "\\int \\frac{4}{x^{9}} \\, dx", "reference_antiderivative": "-1/(2*x**8)", "category": "polynomial", "variable": "x"}
{"id": "atom-0017", "stage": "atomic", "k": 1, "integrand": "-5*x**6", "integrand_latex": "- 5 x^{6}", "integrand_latex_integral": "\\int - 5 x^{6} \\, dx", "reference_antiderivative": "-5*x**7/7", "category": "polynomial", "variable": "x"}
{"id": "atom-0018", "stage": "atomic", "k": 1, "integrand": "-1/x**13", "integrand_latex": "- \\frac{1}{x^{13}}", "integrand_latex_integral": "\\int - \\frac{1}{x^{13}} \\, dx", "reference_antiderivative": "1/(12*x**12)", "category": "polynomial", "variable": "x"}
{"id": "atom-0019", "stage": "atomic", "k": 1, "integrand": "-4/x**3", "integrand_latex": "- \\frac{4}{x^{3}}", "integrand_latex_integral": "\\int - \\frac{4}{x^{3}} \\, dx", "reference_antiderivative": "2/x**2", "category": "polynomial", "variable": "x"}
{"id": "atom-0020", "stage": "atomic", "k": 1, "integrand": "5*x**11", "integrand_latex": "5 x^{11}", "integrand_latex_integral": "\\int 5 x^{11} \\, dx", "reference_antiderivative": "5*x**12/12", "category": "polynomial", "variable": "x"}
{"id": "atom-0021", "stage": "atomic", "k": 1, "integrand": "-2*x**6", "integrand_latex": "- 2 x^{6}", "integrand_latex_integral": "\\int - 2 x^{6} \\, dx", "reference_antiderivative": "-2*x**7/7", "category": "polynomial", "variable": "x"}
{"id": "atom-0022", "stage": "atomic", "k": 1, "integrand": "5*x**5", "integrand_latex": "5 x^{5}", "integrand_latex_integral": "\\int 5 x^{5} \\, dx", "reference_antiderivative": "5*x**6/6", "category": "polynomial", "variable": "x"}
{"id": "atom-0023", "stage": "atomic", "k": 1, "integrand": "5/x**10", "integrand_latex": "\\frac{5}{x^{10}}", "integrand_latex_integral": "\\int \\frac{5}{x^{10}} \\, dx", "reference_antiderivative": "-5/(9*x**9)", "category": "polynomial", "variable": "x"}
{"id": "atom-0024", "stage": "atomic", "k": 1, "integrand": "-2/x**10", "integrand_latex": "- \\frac{2}{x^{10}}", "integrand_latex_integral": "\\int - \\frac{2}{x^{10}} \\, dx", "reference_antiderivative": "2/(9*x**9)", "category": "polynomial", "variable": "x"}
{"id": "atom-0025", "stage": "atomic", "k": 1, "integrand": "-x**14", "integrand_latex": "- x^{14}", "integrand_latex_integral": "\\int - x^{14} \\, dx", "reference_antiderivative": "-x**15/15", "category": "polynomial", "variable": "x"}
{"id": "atom-0026", "stage": "atomic", "k": 1, "integrand": "3/x**8", "integrand_latex": "\\frac{3}{x^{8}}", "integrand_latex_integral": "\\int \\frac{3}{x^{8}} \\, dx", "reference_antiderivative": "-3/(7*x**7)", "category": "polynomial", "variable": "x"}
{"id": "atom-0027", "stage": "atomic", "k": 1, "integrand": "-5/x**8", "integrand_latex": "- \\frac{5}{x^{8}}", "integrand_latex_integral": "\\int - \\frac{5}{x^{8}} \\, dx", "reference_antiderivative": "5/(7*x**7)", "category": "polynomial", "variable": "x"}
{"id": "atom-0028", "stage": "atomic", "k": 1, "integrand": "x**(-7)", "integrand_latex": "\\frac{1}{x^{7}}", "integrand_latex_integral": "\\int \\frac{1}{x^{7}} \\, dx", "reference_antiderivative": "-1/(6*x**6)", "category": "polynomial", "variable": "x"}
{"id": "atom-0029", "stage": "atomic", "k": 1, "integrand": "4*x**13", "integrand_latex": "4 x^{13}", "integrand_latex_integral": "\\int 4 x^{13} \\, dx", "reference_antiderivative": "2*x**14/7", "category": "polynomial", "variable": "x"}
{"id": "atom-0030", "stage": "atomic", "k": 1, "integrand": "-2*x**5", "integrand_latex": "- 2 x^{5}", "integrand_latex_integral": "\\int - 2 x^{5} \\, dx", "reference_antiderivative": "-x**6/3", "category": "polynomial", "variable": "x"}
{"id": "atom-0031", "stage": "atomic", "k": 1, "integrand": "5/x", "integrand_latex": "\\frac{5}{x}", "integrand_latex_integral": "\\int \\frac{5}{x} \\, dx", "reference_antiderivative": "5*log(x)", "category": "polynomial", "variable": "x"}
{"id": "atom-0032", "stage": "atomic", "k": 1, "integrand": "-3/x**8", "integrand_latex": "- \\frac{3}{x^{8}}", "integrand_latex_integral": "\\int - \\frac{3}{x^{8}} \\, dx", "reference_antiderivative": "3/(7*x**7)", "category": "polynomial", "variable": "x"}
{"id": "atom-0033", "stage": "atomic", "k": 1, "integrand": "3/x**7", "integrand_latex": "\\frac{3}{x^{7}}", "integrand_latex_integral": "\\int \\frac{3}{x^{7}} \\, dx", "reference_antiderivative": "-1/(2*x**6)", "category": "polynomial", "variable": "x"}
{"id": "atom-0034", "stage": "atomic", "k": 1, "integrand": "x**13", "integrand_latex": "x^{13}", "integrand_latex_integral": "\\int x^{13} \\, dx", "reference_antiderivative": "x**14/14", "category": "polynomial", "variable": "x"}
{"id": "atom-0035", "stage": "atomic", "k": 1, "integrand": "-4*x**9", "integrand_latex": "- 4 x^{9}", "integrand_latex_integral": "\\int - 4 x^{9} \\, dx", "reference_antiderivative": "-2*x**10/5", "category": "polynomial", "variable": "x"}
{"id": "atom-0036", "stage": "atomic", "k": 1, "integrand": "-4/x**11", "integrand_latex": "- \\frac{4}{x^{11}}", "integrand_latex_integral": "\\int - \\frac{4}{x^{11}} \\, dx", "reference_antiderivative": "2/(5*x**10)", "category": "polynomial", "variable": "x"}
{"id": "atom-0037", "stage": "atomic", "k": 1, "integrand": "5/x**2", "integrand_latex": "\\frac{5}{x^{2}}", "integrand_latex_integral": "\\int \\frac{5}{x^{2}} \\, dx", "reference_antiderivative": "-5/x", "category": "polynomial", "variable": "x"}
{"id": "atom-0038", "stage": "atomic", "k": 1, "integrand": "x**(-3)", "integrand_latex": "\\frac{1}{x^{3}}", "integrand_latex_integral": "\\int \\frac{1}{x^{3}} \\, dx", "reference_antiderivative": "-1/(2*x**2)", "category": "polynomial", "variable": "x"}
{"id": "atom-0039", "stage": "atomic", "k": 1, "integrand": "2*x", "integrand_latex": "2 x", "integrand_latex_integral": "\\int 2 x \\, dx", "reference_antiderivative": "x**2", "category": "polynomial", "variable": "x"}
{"id": "atom-0040", "stage": "atomic", "k": 1, "integrand": "3*x**12", "integrand_latex": "3 x^{12}", "integrand_latex_integral": "\\int 3 x^{12} \\, dx", "reference_antiderivative": "3*x**13/13", "category": "polynomial", "variable": "x"}
{"id": "atom-0041", "stage": "atomic", "k": 1, "integrand": "3*x**9", "integrand_latex": "3 x^{9}", "integrand_latex_integral": "\\int 3 x^{9} \\, dx", "reference_antiderivative": "3*x**10/10", "category": "polynomial", "variable": "x"}
{"id": "atom-0042", "stage": "atomic", "k": 1, "integrand": "5/x**5", "integrand_latex": "\\frac{5}{x^{5}}", "integrand_latex_integral": "\\int \\frac{5}{x^{5}} \\, dx", "reference_antiderivative": "-5/(4*x**4)", "category": "polynomial", "variable": "x"}
{"id": "atom-0043", "stage": "atomic", "k": 1, "integrand": "x**(-10)", "integrand_latex": "\\frac{1}{x^{10}}", "integrand_latex_integral": "\\int \\frac{1}{x^{10}} \\, dx", "reference_antiderivative": "-1/(9*x**9)", "category": "polynomial", "variable": "x"}
{"id": "atom-0044", "stage": "atomic", "k": 1, "integrand": "-x", "integrand_latex": "- x", "integrand_latex_integral": "\\int - x \\, dx", "reference_antiderivative": "-x**2/2", "category": "polynomial", "variable": "x"}
{"id": "atom-0045", "stage": "atomic", "k": 1, "integrand": "3*x**14", "integrand_latex": "3 x^{14}", "integrand_latex_integral": "\\int 3 x^{14} \\, dx", "reference_antiderivative": "x**15/5", "category": "polynomial", "variable": "x"}
{"id": "atom-0046", "stage": "atomic", "k": 1, "integrand": "5/x**6", "integrand_latex": "\\frac{5}{x^{6}}", "integrand_latex_integral": "\\int \\frac{5}{x^{6}} \\, dx", "reference_antiderivative": "-1/x**5", "category": "polynomial", "variable": "x"}
{"id": "atom-0047", "stage": "atomic", "k": 1, "integrand": "-3*x**2", "integrand_latex": "- 3 x^{2}", "integrand_latex_integral": "\\int - 3 x^{2} \\, dx", "reference_antiderivative": "-x**3", "category": "polynomial", "variable": "x"}
{"id": "atom-0048", "stage": "atomic", "k": 1, "integrand": "2/x**15", "integrand_latex": "\\frac{2}{x^{15}}", "integrand_latex_integral": "\\int \\frac{2}{x^{15}} \\, dx", "reference_antiderivative": "-1/(7*x**14)", "category": "polynomial", "variable": "x"}
{"id": "atom-0049", "stage": "atomic", "k": 1, "integrand": "-1/x**8", "integrand_latex": "- \\frac{1}{x^{8}}", "integrand_latex_integral": "\\int - \\frac{1}{x^{8}} \\, dx", "reference_antiderivative": "1/(7*x**7)", "category": "polynomial", "variable": "x"}
{"id": "atom-0050", "stage": "atomic", "k": 1, "integrand": "4*x**15", "integrand_latex": "4 x^{15}", "integrand_latex_integral": "\\int 4 x^{15} \\, dx", "reference_antiderivative": "x**16/4", "category": "polynomial", "variable": "x"}
{"id": "atom-0051", "stage": "atomic", "k": 1, "integrand": "2*x**11", "integrand_latex": "2 x^{11}", "integrand_latex_integral": "\\int 2 x^{11} \\, dx", "reference_antiderivative": "x**12/6", "category": "polynomial", "variable": "x"}
{"id": "atom-0052", "stage": "atomic", "k": 1, "integrand": "5*x**15", "integrand_latex": "5 x^{15}", "integrand_latex_integral": "\\int 5 x^{15} \\, dx", "reference_antiderivative": "5*x**16/16", "category": "polynomial", "variable": "x"}
{"id": "atom-0053", "stage": "atomic", "k": 1, "integrand": "x**15", "integrand_latex": "x^{15}", "integrand_latex_integral": "\\int x^{15} \\, dx", "reference_antiderivative": "x**16/16", "category": "polynomial", "variable": "x"}
{"id": "atom-0054", "stage": "atomic", "k": 1, "integrand": "3/x", "integrand_latex": "\\frac{3}{x}", "integrand_latex_integral": "\\int \\frac{3}{x} \\, dx", "reference_antiderivative": "3*log(x)", "category": "polynomial", "variable": "x"}
{"id": "atom-0055", "stage": "atomic", "k": 1, "integrand": "-2/x**13", "integrand_latex": "- \\frac{2}{x^{13}}", "integrand_latex_integral": "\\int - \\frac{2}{x^{13}} \\, dx", "reference_antiderivative": "1/(6*x**12)", "category": "polynomial", "variable": "x"}
{"id": "atom-0056", "stage": "atomic", "k": 1, "integrand": "4*x**2", "integrand_latex": "4 x^{2}", "integrand_latex_integral": "\\int 4 x^{2} \\, dx", "reference_antiderivative": "4*x**3/3", "category": "polynomial", "variable": "x"}
{"id": "atom-0057", "stage": "atomic", "k": 1, "integrand": "-2/x**15", "integrand_latex": "- \\frac{2}{x^{15}}", "integrand_latex_integral": "\\int - \\frac{2}{x^{15}} \\, dx", "reference_antiderivative": "1/(7*x**14)", "category": "polynomial", "variable": "x"}
{"id": "atom-0058", "stage": "atomic", "k": 1, "integrand": "5/x**14", "integrand_latex": "\\frac{5}{x^{14}}", "integrand_latex_integral": "\\int \\frac{5}{x^{14}} \\, dx", "reference_antiderivative": "-5/(13*x**13)", "category": "polynomial", "variable": "x"}
{"id": "atom-0059", "stage": "atomic", "k": 1, "integrand": "-5*x**12", "integrand_latex": "- 5 x^{12}", "integrand_latex_integral": "\\int - 5 x^{12} \\, dx", "reference_antiderivative": "-5*x**13/13", "category": "polynomial", "variable": "x"}
{"id": "atom-0060", "stage": "atomic", "k": 1, "integrand": "2/x**9", "integrand_latex": "\\frac{2}{x^{9}}", "integrand_latex_integral": "\\int \\frac{2}{x^{9}} \\, dx", "reference_antiderivative": "-1/(4*x**8)", "category": "polynomial", "variable": "x"}
{"id": "atom-0061", "stage": "atomic", "k": 1, "integrand": "4*x**3", "integrand_latex": "4 x^{3}", "integrand_latex_integral": "\\int 4 x^{3} \\, dx", "reference_antiderivative": "x**4", "category": "polynomial", "variable": "x"}
{"id": "atom-0062", "stage": "atomic", "k": 1, "integrand": "2*x**10", "integrand_latex": "2 x^{10}", "integrand_latex_integral": "\\int 2 x^{10} \\, dx", "reference_antiderivative": "2*x**11/11", "category": "polynomial", "variable": "x"}
{"id": "atom-0063", "stage": "atomic", "k": 1, "integrand": "-4/x**12", "integrand_latex": "- \\frac{4}{x^{12}}", "integrand_latex_integral": "\\int - \\frac{4}{x^{12}} \\, dx", "reference_antiderivative": "4/(11*x**11)", "category": "polynomial", "variable": "x"}
{"id": "atom-0064", "stage": "atomic", "k": 1, "integrand": "x**(-2)", "integrand_latex": "\\frac{1}{x^{2}}", "integrand_latex_integral": "\\int \\frac{1}{x^{2}} \\, dx", "reference_antiderivative": "-1/x", "category": "polynomial", "variable": "x"}
{"id": "atom-0065", "stage": "atomic", "k": 1, "integrand": "5/x**12", "integrand_latex": "\\frac{5}{x^{12}}", "integrand_latex_integral": "\\int \\frac{5}{x^{12}} \\, dx", "reference_antiderivative": "-5/(11*x**11)", "category": "polynomial", "variable": "x"}
{"id": "atom-0066", "stage": "atomic", "k": 1, "integrand": "-4/x**8", "integrand_latex": "- \\frac{4}{x^{8}}", "integrand_latex_integral": "\\int - \\frac{4}{x^{8}} \\, dx", "reference_antiderivative": "4/(7*x**7)", "category": "polynomial", "variable": "x"}
{"id": "atom-0067", "stage": "atomic", "k": 1, "integrand": "-3/x**7", "integrand_latex": "- \\frac{3}{x^{7}}", "integrand_latex_integral": "\\int - \\frac{3}{x^{7}} \\, dx", "reference_antiderivative": "1/(2*x**6)", "category": "polynomial", "variable": "x"}
{"id": "atom-0068", "stage": "atomic", "k": 1, "integrand": "-4/x", "integrand_latex": "- \\frac{4}{x}", "integrand_latex_integral": "\\int - \\frac{4}{x} \\, dx", "reference_antiderivative": "-4*log(x)", "category": "polynomial", "variable": "x"}
{"id": "atom-0069", "stage": "atomic", "k": 1, "integrand": "3/x**12", "integrand_latex": "\\frac{3}{x^{12}}", "integrand_latex_integral": "\\int \\frac{3}{x^{12}} \\, dx", "reference_antiderivative": "-3/(11*x**11)", "category": "polynomial", "variable": "x"}
{"id": "atom-0070", "stage": "atomic", "k": 1, "integrand": "3*x**11", "integrand_latex": "3 x^{11}", "integrand_latex_integral": "\\int 3 x^{11} \\, dx", "reference_antiderivative": "x**12/4", "category": "polynomial", "variable": "x"}
{"id": "atom-0071", "stage": "atomic", "k": 1, "integrand": "-4*x**14", "integrand_latex": "- 4 x^{14}", "integrand_latex_integral": "\\int - 4 x^{14} \\, dx", "reference_antiderivative": "-4*x**15/15", "category": "polynomial", "variable": "x"}
{"id": "atom-0072", "stage": "atomic", "k": 1, "integrand": "-5/x**10", "integrand_latex": "- \\frac{5}{x^{10}}", "integrand_latex_integral": "\\int - \\frac{5}{x^{10}} \\, dx", "reference_antiderivative": "5/(9*x**9)", "category": "polynomial", "variable": "x"}
{"id": "atom-0073", "stage": "atomic", "k": 1, "integrand": "2/x**6", "integrand_latex": "\\frac{2}{x^{6}}", "integrand_latex_integral": "\\int \\frac{2}{x^{6}} \\, dx", "reference_antiderivative": "-2/(5*x**5)", "category": "polynomial", "variable": "x"}
{"id": "atom-0074", "stage": "atomic", "k": 1, "integrand": "3*x**6", "integrand_latex": "3 x^{6}", "integrand_latex_integral": "\\int 3 x^{6} \\, dx", "reference_antiderivative": "3*x**7/7", "category": "polynomial", "variable": "x"}
{"id": "atom-0075", "stage": "atomic", "k": 1, "integrand": "-3/x**9", "integrand_latex": "- \\frac{3}{x^{9}}", "integrand_latex_integral": "\\int - \\frac{3}{x^{9}} \\, dx", "reference_antiderivative": "3/(8*x**8)", "category": "polynomial", "variable": "x"}
{"id": "atom-0076", "stage": "atomic", "k": 1, "integrand": "-5*x**3", "integrand_latex": "- 5 x^{3}", "integrand_latex_integral": "\\int - 5 x^{3} \\, dx", "reference_antiderivative": "-5*x**4/4", "category": "polynomial", "variable": "x"}
{"id": "atom-0077", "stage": "atomic", "k": 1, "integrand": "3/x**10", "integrand_latex": "\\frac{3}{x^{10}}", "integrand_latex_integral": "\\int \\frac{3}{x^{10}} \\, dx", "reference_antiderivative": "-1/(3*x**9)", "category": "polynomial", "variable": "x"}
{"id": "atom-0078", "stage": "atomic", "k": 1, "integrand": "3/x**13", "integrand_latex": "\\frac{3}{x^{13}}", "integrand_latex_integral": "\\int \\frac{3}{x^{13}} \\, dx", "reference_antiderivative": "-1/(4*x**12)", "category": "polynomial", "variable": "x"}
{"id": "atom-0079", "stage": "atomic", "k": 1, "integrand": "-4*x**4", "integrand_latex": "- 4 x^{4}", "integrand_latex_integral": "\\int - 4 x^{4} \\, dx", "reference_antiderivative": "-4*x**5/5", "category": "polynomial", "variable": "x"}
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{"id": "atom-0158", "stage": "atomic", "k": 1, "integrand": "5/x**7", "integrand_latex": "\\frac{5}{x^{7}}", "integrand_latex_integral": "\\int \\frac{5}{x^{7}} \\, dx", "reference_antiderivative": "-5/(6*x**6)", "category": "polynomial", "variable": "x"}
{"id": "atom-0159", "stage": "atomic", "k": 1, "integrand": "-1/x**5", "integrand_latex": "- \\frac{1}{x^{5}}", "integrand_latex_integral": "\\int - \\frac{1}{x^{5}} \\, dx", "reference_antiderivative": "1/(4*x**4)", "category": "polynomial", "variable": "x"}
{"id": "atom-0160", "stage": "atomic", "k": 1, "integrand": "-4/x**7", "integrand_latex": "- \\frac{4}{x^{7}}", "integrand_latex_integral": "\\int - \\frac{4}{x^{7}} \\, dx", "reference_antiderivative": "2/(3*x**6)", "category": "polynomial", "variable": "x"}
{"id": "atom-0161", "stage": "atomic", "k": 1, "integrand": "-2*x**9", "integrand_latex": "- 2 x^{9}", "integrand_latex_integral": "\\int - 2 x^{9} \\, dx", "reference_antiderivative": "-x**10/5", "category": "polynomial", "variable": "x"}
{"id": "atom-0162", "stage": "atomic", "k": 1, "integrand": "4*x**6", "integrand_latex": "4 x^{6}", "integrand_latex_integral": "\\int 4 x^{6} \\, dx", "reference_antiderivative": "4*x**7/7", "category": "polynomial", "variable": "x"}
{"id": "atom-0163", "stage": "atomic", "k": 1, "integrand": "4*x**7", "integrand_latex": "4 x^{7}", "integrand_latex_integral": "\\int 4 x^{7} \\, dx", "reference_antiderivative": "x**8/2", "category": "polynomial", "variable": "x"}
{"id": "atom-0164", "stage": "atomic", "k": 1, "integrand": "3/x**15", "integrand_latex": "\\frac{3}{x^{15}}", "integrand_latex_integral": "\\int \\frac{3}{x^{15}} \\, dx", "reference_antiderivative": "-3/(14*x**14)", "category": "polynomial", "variable": "x"}
{"id": "atom-0165", "stage": "atomic", "k": 1, "integrand": "2*x**5", "integrand_latex": "2 x^{5}", "integrand_latex_integral": "\\int 2 x^{5} \\, dx", "reference_antiderivative": "x**6/3", "category": "polynomial", "variable": "x"}
{"id": "atom-0166", "stage": "atomic", "k": 1, "integrand": "-2/x**6", "integrand_latex": "- \\frac{2}{x^{6}}", "integrand_latex_integral": "\\int - \\frac{2}{x^{6}} \\, dx", "reference_antiderivative": "2/(5*x**5)", "category": "polynomial", "variable": "x"}
{"id": "atom-0167", "stage": "atomic", "k": 1, "integrand": "x**8", "integrand_latex": "x^{8}", "integrand_latex_integral": "\\int x^{8} \\, dx", "reference_antiderivative": "x**9/9", "category": "polynomial", "variable": "x"}
{"id": "atom-0168", "stage": "atomic", "k": 1, "integrand": "2/x**7", "integrand_latex": "\\frac{2}{x^{7}}", "integrand_latex_integral": "\\int \\frac{2}{x^{7}} \\, dx", "reference_antiderivative": "-1/(3*x**6)", "category": "polynomial", "variable": "x"}
{"id": "atom-0169", "stage": "atomic", "k": 1, "integrand": "-2/x**12", "integrand_latex": "- \\frac{2}{x^{12}}", "integrand_latex_integral": "\\int - \\frac{2}{x^{12}} \\, dx", "reference_antiderivative": "2/(11*x**11)", "category": "polynomial", "variable": "x"}
{"id": "atom-0170", "stage": "atomic", "k": 1, "integrand": "-2/x**4", "integrand_latex": "- \\frac{2}{x^{4}}", "integrand_latex_integral": "\\int - \\frac{2}{x^{4}} \\, dx", "reference_antiderivative": "2/(3*x**3)", "category": "polynomial", "variable": "x"}
{"id": "atom-0171", "stage": "atomic", "k": 1, "integrand": "-5*x**7", "integrand_latex": "- 5 x^{7}", "integrand_latex_integral": "\\int - 5 x^{7} \\, dx", "reference_antiderivative": "-5*x**8/8", "category": "polynomial", "variable": "x"}
{"id": "atom-0172", "stage": "atomic", "k": 1, "integrand": "2/x**12", "integrand_latex": "\\frac{2}{x^{12}}", "integrand_latex_integral": "\\int \\frac{2}{x^{12}} \\, dx", "reference_antiderivative": "-2/(11*x**11)", "category": "polynomial", "variable": "x"}
{"id": "atom-0173", "stage": "atomic", "k": 1, "integrand": "4/x**6", "integrand_latex": "\\frac{4}{x^{6}}", "integrand_latex_integral": "\\int \\frac{4}{x^{6}} \\, dx", "reference_antiderivative": "-4/(5*x**5)", "category": "polynomial", "variable": "x"}
{"id": "atom-0174", "stage": "atomic", "k": 1, "integrand": "2/x**5", "integrand_latex": "\\frac{2}{x^{5}}", "integrand_latex_integral": "\\int \\frac{2}{x^{5}} \\, dx", "reference_antiderivative": "-1/(2*x**4)", "category": "polynomial", "variable": "x"}
{"id": "atom-0175", "stage": "atomic", "k": 1, "integrand": "1/x", "integrand_latex": "\\frac{1}{x}", "integrand_latex_integral": "\\int \\frac{1}{x} \\, dx", "reference_antiderivative": "log(x)", "category": "polynomial", "variable": "x"}
{"id": "atom-0176", "stage": "atomic", "k": 1, "integrand": "x**(-6)", "integrand_latex": "\\frac{1}{x^{6}}", "integrand_latex_integral": "\\int \\frac{1}{x^{6}} \\, dx", "reference_antiderivative": "-1/(5*x**5)", "category": "polynomial", "variable": "x"}
{"id": "atom-0177", "stage": "atomic", "k": 1, "integrand": "-4/x**10", "integrand_latex": "- \\frac{4}{x^{10}}", "integrand_latex_integral": "\\int - \\frac{4}{x^{10}} \\, dx", "reference_antiderivative": "4/(9*x**9)", "category": "polynomial", "variable": "x"}
{"id": "atom-0178", "stage": "atomic", "k": 1, "integrand": "-x**7", "integrand_latex": "- x^{7}", "integrand_latex_integral": "\\int - x^{7} \\, dx", "reference_antiderivative": "-x**8/8", "category": "polynomial", "variable": "x"}
{"id": "atom-0179", "stage": "atomic", "k": 1, "integrand": "-x**10", "integrand_latex": "- x^{10}", "integrand_latex_integral": "\\int - x^{10} \\, dx", "reference_antiderivative": "-x**11/11", "category": "polynomial", "variable": "x"}
{"id": "atom-0180", "stage": "atomic", "k": 1, "integrand": "-2/x**2", "integrand_latex": "- \\frac{2}{x^{2}}", "integrand_latex_integral": "\\int - \\frac{2}{x^{2}} \\, dx", "reference_antiderivative": "2/x", "category": "polynomial", "variable": "x"}
{"id": "atom-0181", "stage": "atomic", "k": 1, "integrand": "-x**11", "integrand_latex": "- x^{11}", "integrand_latex_integral": "\\int - x^{11} \\, dx", "reference_antiderivative": "-x**12/12", "category": "polynomial", "variable": "x"}
{"id": "atom-0182", "stage": "atomic", "k": 1, "integrand": "-1/x", "integrand_latex": "- \\frac{1}{x}", "integrand_latex_integral": "\\int - \\frac{1}{x} \\, dx", "reference_antiderivative": "-log(x)", "category": "polynomial", "variable": "x"}
{"id": "atom-0183", "stage": "atomic", "k": 1, "integrand": "-1/x**15", "integrand_latex": "- \\frac{1}{x^{15}}", "integrand_latex_integral": "\\int - \\frac{1}{x^{15}} \\, dx", "reference_antiderivative": "1/(14*x**14)", "category": "polynomial", "variable": "x"}
{"id": "atom-0184", "stage": "atomic", "k": 1, "integrand": "x**5", "integrand_latex": "x^{5}", "integrand_latex_integral": "\\int x^{5} \\, dx", "reference_antiderivative": "x**6/6", "category": "polynomial", "variable": "x"}
{"id": "atom-0185", "stage": "atomic", "k": 1, "integrand": "-4/x**4", "integrand_latex": "- \\frac{4}{x^{4}}", "integrand_latex_integral": "\\int - \\frac{4}{x^{4}} \\, dx", "reference_antiderivative": "4/(3*x**3)", "category": "polynomial", "variable": "x"}
{"id": "atom-0186", "stage": "atomic", "k": 1, "integrand": "3/x**14", "integrand_latex": "\\frac{3}{x^{14}}", "integrand_latex_integral": "\\int \\frac{3}{x^{14}} \\, dx", "reference_antiderivative": "-3/(13*x**13)", "category": "polynomial", "variable": "x"}
{"id": "atom-0187", "stage": "atomic", "k": 1, "integrand": "x**12", "integrand_latex": "x^{12}", "integrand_latex_integral": "\\int x^{12} \\, dx", "reference_antiderivative": "x**13/13", "category": "polynomial", "variable": "x"}
{"id": "atom-0188", "stage": "atomic", "k": 1, "integrand": "2/x**2", "integrand_latex": "\\frac{2}{x^{2}}", "integrand_latex_integral": "\\int \\frac{2}{x^{2}} \\, dx", "reference_antiderivative": "-2/x", "category": "polynomial", "variable": "x"}
{"id": "atom-0189", "stage": "atomic", "k": 1, "integrand": "3/x**4", "integrand_latex": "\\frac{3}{x^{4}}", "integrand_latex_integral": "\\int \\frac{3}{x^{4}} \\, dx", "reference_antiderivative": "-1/x**3", "category": "polynomial", "variable": "x"}
{"id": "atom-0190", "stage": "atomic", "k": 1, "integrand": "-5/x**9", "integrand_latex": "- \\frac{5}{x^{9}}", "integrand_latex_integral": "\\int - \\frac{5}{x^{9}} \\, dx", "reference_antiderivative": "5/(8*x**8)", "category": "polynomial", "variable": "x"}
{"id": "atom-0191", "stage": "atomic", "k": 1, "integrand": "-3*x**14", "integrand_latex": "- 3 x^{14}", "integrand_latex_integral": "\\int - 3 x^{14} \\, dx", "reference_antiderivative": "-x**15/5", "category": "polynomial", "variable": "x"}
{"id": "atom-0192", "stage": "atomic", "k": 1, "integrand": "-3/x**6", "integrand_latex": "- \\frac{3}{x^{6}}", "integrand_latex_integral": "\\int - \\frac{3}{x^{6}} \\, dx", "reference_antiderivative": "3/(5*x**5)", "category": "polynomial", "variable": "x"}
{"id": "atom-0193", "stage": "atomic", "k": 1, "integrand": "-3/x**3", "integrand_latex": "- \\frac{3}{x^{3}}", "integrand_latex_integral": "\\int - \\frac{3}{x^{3}} \\, dx", "reference_antiderivative": "3/(2*x**2)", "category": "polynomial", "variable": "x"}
{"id": "atom-0194", "stage": "atomic", "k": 1, "integrand": "4*x", "integrand_latex": "4 x", "integrand_latex_integral": "\\int 4 x \\, dx", "reference_antiderivative": "2*x**2", "category": "polynomial", "variable": "x"}
{"id": "atom-0195", "stage": "atomic", "k": 1, "integrand": "-x**8", "integrand_latex": "- x^{8}", "integrand_latex_integral": "\\int - x^{8} \\, dx", "reference_antiderivative": "-x**9/9", "category": "polynomial", "variable": "x"}
{"id": "atom-0196", "stage": "atomic", "k": 1, "integrand": "2*x**12", "integrand_latex": "2 x^{12}", "integrand_latex_integral": "\\int 2 x^{12} \\, dx", "reference_antiderivative": "2*x**13/13", "category": "polynomial", "variable": "x"}
{"id": "atom-0197", "stage": "atomic", "k": 1, "integrand": "3/x**3", "integrand_latex": "\\frac{3}{x^{3}}", "integrand_latex_integral": "\\int \\frac{3}{x^{3}} \\, dx", "reference_antiderivative": "-3/(2*x**2)", "category": "polynomial", "variable": "x"}
{"id": "atom-0198", "stage": "atomic", "k": 1, "integrand": "x**(-8)", "integrand_latex": "\\frac{1}{x^{8}}", "integrand_latex_integral": "\\int \\frac{1}{x^{8}} \\, dx", "reference_antiderivative": "-1/(7*x**7)", "category": "polynomial", "variable": "x"}
{"id": "atom-0199", "stage": "atomic", "k": 1, "integrand": "x**(-14)", "integrand_latex": "\\frac{1}{x^{14}}", "integrand_latex_integral": "\\int \\frac{1}{x^{14}} \\, dx", "reference_antiderivative": "-1/(13*x**13)", "category": "polynomial", "variable": "x"}
{"id": "atom-0200", "stage": "atomic", "k": 1, "integrand": "2*cos(7*x + 14)", "integrand_latex": "2 \\cos{\\left(7 x + 14 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(7 x + 14 \\right)} \\, dx", "reference_antiderivative": "2*sin(7*x + 14)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0201", "stage": "atomic", "k": 1, "integrand": "5*tan(10*x + 11)", "integrand_latex": "5 \\tan{\\left(10 x + 11 \\right)}", "integrand_latex_integral": "\\int 5 \\tan{\\left(10 x + 11 \\right)} \\, dx", "reference_antiderivative": "log(tan(10*x + 11)**2 + 1)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0202", "stage": "atomic", "k": 1, "integrand": "2*sin(15*x - 14)", "integrand_latex": "2 \\sin{\\left(15 x - 14 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(15 x - 14 \\right)} \\, dx", "reference_antiderivative": "-2*cos(15*x - 14)/15", "category": "trigonometric", "variable": "x"}
{"id": "atom-0203", "stage": "atomic", "k": 1, "integrand": "-4*sin(5*x - 12)", "integrand_latex": "- 4 \\sin{\\left(5 x - 12 \\right)}", "integrand_latex_integral": "\\int - 4 \\sin{\\left(5 x - 12 \\right)} \\, dx", "reference_antiderivative": "4*cos(5*x - 12)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0204", "stage": "atomic", "k": 1, "integrand": "2*cos(12*x - 1)", "integrand_latex": "2 \\cos{\\left(12 x - 1 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(12 x - 1 \\right)} \\, dx", "reference_antiderivative": "sin(12*x - 1)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0205", "stage": "atomic", "k": 1, "integrand": "3*tan(2*x - 12)", "integrand_latex": "3 \\tan{\\left(2 x - 12 \\right)}", "integrand_latex_integral": "\\int 3 \\tan{\\left(2 x - 12 \\right)} \\, dx", "reference_antiderivative": "3*log(tan(2*x - 12)**2 + 1)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0206", "stage": "atomic", "k": 1, "integrand": "-4*cos(10*x - 7)", "integrand_latex": "- 4 \\cos{\\left(10 x - 7 \\right)}", "integrand_latex_integral": "\\int - 4 \\cos{\\left(10 x - 7 \\right)} \\, dx", "reference_antiderivative": "-2*sin(10*x - 7)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0207", "stage": "atomic", "k": 1, "integrand": "cos(5*x - 13)", "integrand_latex": "\\cos{\\left(5 x - 13 \\right)}", "integrand_latex_integral": "\\int \\cos{\\left(5 x - 13 \\right)} \\, dx", "reference_antiderivative": "sin(5*x - 13)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0208", "stage": "atomic", "k": 1, "integrand": "3*cos(3*x - 15)", "integrand_latex": "3 \\cos{\\left(3 x - 15 \\right)}", "integrand_latex_integral": "\\int 3 \\cos{\\left(3 x - 15 \\right)} \\, dx", "reference_antiderivative": "sin(3*x - 15)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0209", "stage": "atomic", "k": 1, "integrand": "2*sin(12*x + 2)", "integrand_latex": "2 \\sin{\\left(12 x + 2 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(12 x + 2 \\right)} \\, dx", "reference_antiderivative": "-cos(12*x + 2)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0210", "stage": "atomic", "k": 1, "integrand": "-2*cos(5*x + 6)", "integrand_latex": "- 2 \\cos{\\left(5 x + 6 \\right)}", "integrand_latex_integral": "\\int - 2 \\cos{\\left(5 x + 6 \\right)} \\, dx", "reference_antiderivative": "-2*sin(5*x + 6)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0211", "stage": "atomic", "k": 1, "integrand": "4*tan(2*x + 12)", "integrand_latex": "4 \\tan{\\left(2 x + 12 \\right)}", "integrand_latex_integral": "\\int 4 \\tan{\\left(2 x + 12 \\right)} \\, dx", "reference_antiderivative": "log(tan(2*x + 12)**2 + 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0212", "stage": "atomic", "k": 1, "integrand": "4*tan(x + 10)", "integrand_latex": "4 \\tan{\\left(x + 10 \\right)}", "integrand_latex_integral": "\\int 4 \\tan{\\left(x + 10 \\right)} \\, dx", "reference_antiderivative": "2*log(tan(x + 10)**2 + 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0213", "stage": "atomic", "k": 1, "integrand": "5*sin(14*x + 5)", "integrand_latex": "5 \\sin{\\left(14 x + 5 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(14 x + 5 \\right)} \\, dx", "reference_antiderivative": "-5*cos(14*x + 5)/14", "category": "trigonometric", "variable": "x"}
{"id": "atom-0214", "stage": "atomic", "k": 1, "integrand": "-tan(11*x + 8)", "integrand_latex": "- \\tan{\\left(11 x + 8 \\right)}", "integrand_latex_integral": "\\int - \\tan{\\left(11 x + 8 \\right)} \\, dx", "reference_antiderivative": "-log(tan(11*x + 8)**2 + 1)/22", "category": "trigonometric", "variable": "x"}
{"id": "atom-0215", "stage": "atomic", "k": 1, "integrand": "5*sin(10*x - 10)", "integrand_latex": "5 \\sin{\\left(10 x - 10 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(10 x - 10 \\right)} \\, dx", "reference_antiderivative": "-cos(10*x - 10)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0216", "stage": "atomic", "k": 1, "integrand": "4*tan(12*x - 3)", "integrand_latex": "4 \\tan{\\left(12 x - 3 \\right)}", "integrand_latex_integral": "\\int 4 \\tan{\\left(12 x - 3 \\right)} \\, dx", "reference_antiderivative": "log(tan(12*x - 3)**2 + 1)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0217", "stage": "atomic", "k": 1, "integrand": "2*sin(14*x + 3)", "integrand_latex": "2 \\sin{\\left(14 x + 3 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(14 x + 3 \\right)} \\, dx", "reference_antiderivative": "-cos(14*x + 3)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0218", "stage": "atomic", "k": 1, "integrand": "5*cos(7*x + 1)", "integrand_latex": "5 \\cos{\\left(7 x + 1 \\right)}", "integrand_latex_integral": "\\int 5 \\cos{\\left(7 x + 1 \\right)} \\, dx", "reference_antiderivative": "5*sin(7*x + 1)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0219", "stage": "atomic", "k": 1, "integrand": "2*tan(13*x - 6)", "integrand_latex": "2 \\tan{\\left(13 x - 6 \\right)}", "integrand_latex_integral": "\\int 2 \\tan{\\left(13 x - 6 \\right)} \\, dx", "reference_antiderivative": "log(tan(13*x - 6)**2 + 1)/13", "category": "trigonometric", "variable": "x"}
{"id": "atom-0220", "stage": "atomic", "k": 1, "integrand": "-4*cos(x - 15)", "integrand_latex": "- 4 \\cos{\\left(x - 15 \\right)}", "integrand_latex_integral": "\\int - 4 \\cos{\\left(x - 15 \\right)} \\, dx", "reference_antiderivative": "-4*sin(x - 15)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0221", "stage": "atomic", "k": 1, "integrand": "-cos(5*x + 15)", "integrand_latex": "- \\cos{\\left(5 x + 15 \\right)}", "integrand_latex_integral": "\\int - \\cos{\\left(5 x + 15 \\right)} \\, dx", "reference_antiderivative": "-sin(5*x + 15)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0222", "stage": "atomic", "k": 1, "integrand": "2*sin(12*x - 6)", "integrand_latex": "2 \\sin{\\left(12 x - 6 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(12 x - 6 \\right)} \\, dx", "reference_antiderivative": "-cos(12*x - 6)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0223", "stage": "atomic", "k": 1, "integrand": "2*cos(12*x + 8)", "integrand_latex": "2 \\cos{\\left(12 x + 8 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(12 x + 8 \\right)} \\, dx", "reference_antiderivative": "sin(12*x + 8)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0224", "stage": "atomic", "k": 1, "integrand": "4*cos(6*x - 7)", "integrand_latex": "4 \\cos{\\left(6 x - 7 \\right)}", "integrand_latex_integral": "\\int 4 \\cos{\\left(6 x - 7 \\right)} \\, dx", "reference_antiderivative": "2*sin(6*x - 7)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0225", "stage": "atomic", "k": 1, "integrand": "-5*sin(3*x + 7)", "integrand_latex": "- 5 \\sin{\\left(3 x + 7 \\right)}", "integrand_latex_integral": "\\int - 5 \\sin{\\left(3 x + 7 \\right)} \\, dx", "reference_antiderivative": "5*cos(3*x + 7)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0226", "stage": "atomic", "k": 1, "integrand": "5*sin(9*x + 8)", "integrand_latex": "5 \\sin{\\left(9 x + 8 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(9 x + 8 \\right)} \\, dx", "reference_antiderivative": "-5*cos(9*x + 8)/9", "category": "trigonometric", "variable": "x"}
{"id": "atom-0227", "stage": "atomic", "k": 1, "integrand": "2*cos(11*x + 13)", "integrand_latex": "2 \\cos{\\left(11 x + 13 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(11 x + 13 \\right)} \\, dx", "reference_antiderivative": "2*sin(11*x + 13)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0228", "stage": "atomic", "k": 1, "integrand": "-2*cos(4*x + 10)", "integrand_latex": "- 2 \\cos{\\left(4 x + 10 \\right)}", "integrand_latex_integral": "\\int - 2 \\cos{\\left(4 x + 10 \\right)} \\, dx", "reference_antiderivative": "-sin(4*x + 10)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0229", "stage": "atomic", "k": 1, "integrand": "-2*tan(4*x - 7)", "integrand_latex": "- 2 \\tan{\\left(4 x - 7 \\right)}", "integrand_latex_integral": "\\int - 2 \\tan{\\left(4 x - 7 \\right)} \\, dx", "reference_antiderivative": "-log(tan(4*x - 7)**2 + 1)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0230", "stage": "atomic", "k": 1, "integrand": "5*sin(6*x + 11)", "integrand_latex": "5 \\sin{\\left(6 x + 11 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(6 x + 11 \\right)} \\, dx", "reference_antiderivative": "-5*cos(6*x + 11)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0231", "stage": "atomic", "k": 1, "integrand": "5*cos(5*x - 14)", "integrand_latex": "5 \\cos{\\left(5 x - 14 \\right)}", "integrand_latex_integral": "\\int 5 \\cos{\\left(5 x - 14 \\right)} \\, dx", "reference_antiderivative": "sin(5*x - 14)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0232", "stage": "atomic", "k": 1, "integrand": "-5*tan(3*x - 4)", "integrand_latex": "- 5 \\tan{\\left(3 x - 4 \\right)}", "integrand_latex_integral": "\\int - 5 \\tan{\\left(3 x - 4 \\right)} \\, dx", "reference_antiderivative": "-5*log(tan(3*x - 4)**2 + 1)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0233", "stage": "atomic", "k": 1, "integrand": "-cos(5*x - 8)", "integrand_latex": "- \\cos{\\left(5 x - 8 \\right)}", "integrand_latex_integral": "\\int - \\cos{\\left(5 x - 8 \\right)} \\, dx", "reference_antiderivative": "-sin(5*x - 8)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0234", "stage": "atomic", "k": 1, "integrand": "-3*cos(10*x + 2)", "integrand_latex": "- 3 \\cos{\\left(10 x + 2 \\right)}", "integrand_latex_integral": "\\int - 3 \\cos{\\left(10 x + 2 \\right)} \\, dx", "reference_antiderivative": "-3*sin(10*x + 2)/10", "category": "trigonometric", "variable": "x"}
{"id": "atom-0235", "stage": "atomic", "k": 1, "integrand": "-cos(11*x - 10)", "integrand_latex": "- \\cos{\\left(11 x - 10 \\right)}", "integrand_latex_integral": "\\int - \\cos{\\left(11 x - 10 \\right)} \\, dx", "reference_antiderivative": "-sin(11*x - 10)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0236", "stage": "atomic", "k": 1, "integrand": "2*cos(15*x + 10)", "integrand_latex": "2 \\cos{\\left(15 x + 10 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(15 x + 10 \\right)} \\, dx", "reference_antiderivative": "2*sin(15*x + 10)/15", "category": "trigonometric", "variable": "x"}
{"id": "atom-0237", "stage": "atomic", "k": 1, "integrand": "4*sin(x - 15)", "integrand_latex": "4 \\sin{\\left(x - 15 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(x - 15 \\right)} \\, dx", "reference_antiderivative": "-4*cos(x - 15)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0238", "stage": "atomic", "k": 1, "integrand": "-2*tan(12*x + 6)", "integrand_latex": "- 2 \\tan{\\left(12 x + 6 \\right)}", "integrand_latex_integral": "\\int - 2 \\tan{\\left(12 x + 6 \\right)} \\, dx", "reference_antiderivative": "-log(tan(12*x + 6)**2 + 1)/12", "category": "trigonometric", "variable": "x"}
{"id": "atom-0239", "stage": "atomic", "k": 1, "integrand": "tan(15*x + 12)", "integrand_latex": "\\tan{\\left(15 x + 12 \\right)}", "integrand_latex_integral": "\\int \\tan{\\left(15 x + 12 \\right)} \\, dx", "reference_antiderivative": "log(tan(15*x + 12)**2 + 1)/30", "category": "trigonometric", "variable": "x"}
{"id": "atom-0240", "stage": "atomic", "k": 1, "integrand": "-tan(15*x + 7)", "integrand_latex": "- \\tan{\\left(15 x + 7 \\right)}", "integrand_latex_integral": "\\int - \\tan{\\left(15 x + 7 \\right)} \\, dx", "reference_antiderivative": "-log(tan(15*x + 7)**2 + 1)/30", "category": "trigonometric", "variable": "x"}
{"id": "atom-0241", "stage": "atomic", "k": 1, "integrand": "5*cos(8*x + 6)", "integrand_latex": "5 \\cos{\\left(8 x + 6 \\right)}", "integrand_latex_integral": "\\int 5 \\cos{\\left(8 x + 6 \\right)} \\, dx", "reference_antiderivative": "5*sin(8*x + 6)/8", "category": "trigonometric", "variable": "x"}
{"id": "atom-0242", "stage": "atomic", "k": 1, "integrand": "5*sin(15*x - 4)", "integrand_latex": "5 \\sin{\\left(15 x - 4 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(15 x - 4 \\right)} \\, dx", "reference_antiderivative": "-cos(15*x - 4)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0243", "stage": "atomic", "k": 1, "integrand": "-2*tan(15*x - 4)", "integrand_latex": "- 2 \\tan{\\left(15 x - 4 \\right)}", "integrand_latex_integral": "\\int - 2 \\tan{\\left(15 x - 4 \\right)} \\, dx", "reference_antiderivative": "-log(tan(15*x - 4)**2 + 1)/15", "category": "trigonometric", "variable": "x"}
{"id": "atom-0244", "stage": "atomic", "k": 1, "integrand": "-4*sin(8*x - 5)", "integrand_latex": "- 4 \\sin{\\left(8 x - 5 \\right)}", "integrand_latex_integral": "\\int - 4 \\sin{\\left(8 x - 5 \\right)} \\, dx", "reference_antiderivative": "cos(8*x - 5)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0245", "stage": "atomic", "k": 1, "integrand": "2*cos(14*x + 7)", "integrand_latex": "2 \\cos{\\left(14 x + 7 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(14 x + 7 \\right)} \\, dx", "reference_antiderivative": "sin(14*x + 7)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0246", "stage": "atomic", "k": 1, "integrand": "4*sin(11*x + 14)", "integrand_latex": "4 \\sin{\\left(11 x + 14 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(11 x + 14 \\right)} \\, dx", "reference_antiderivative": "-4*cos(11*x + 14)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0247", "stage": "atomic", "k": 1, "integrand": "-2*sin(12*x + 12)", "integrand_latex": "- 2 \\sin{\\left(12 x + 12 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(12 x + 12 \\right)} \\, dx", "reference_antiderivative": "cos(12*x + 12)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0248", "stage": "atomic", "k": 1, "integrand": "-3*cos(3*x + 1)", "integrand_latex": "- 3 \\cos{\\left(3 x + 1 \\right)}", "integrand_latex_integral": "\\int - 3 \\cos{\\left(3 x + 1 \\right)} \\, dx", "reference_antiderivative": "-sin(3*x + 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0249", "stage": "atomic", "k": 1, "integrand": "-3*tan(2*x - 3)", "integrand_latex": "- 3 \\tan{\\left(2 x - 3 \\right)}", "integrand_latex_integral": "\\int - 3 \\tan{\\left(2 x - 3 \\right)} \\, dx", "reference_antiderivative": "-3*log(tan(2*x - 3)**2 + 1)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0250", "stage": "atomic", "k": 1, "integrand": "cos(5*x - 12)", "integrand_latex": "\\cos{\\left(5 x - 12 \\right)}", "integrand_latex_integral": "\\int \\cos{\\left(5 x - 12 \\right)} \\, dx", "reference_antiderivative": "sin(5*x - 12)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0251", "stage": "atomic", "k": 1, "integrand": "-cos(14*x - 7)", "integrand_latex": "- \\cos{\\left(14 x - 7 \\right)}", "integrand_latex_integral": "\\int - \\cos{\\left(14 x - 7 \\right)} \\, dx", "reference_antiderivative": "-sin(14*x - 7)/14", "category": "trigonometric", "variable": "x"}
{"id": "atom-0252", "stage": "atomic", "k": 1, "integrand": "2*cos(15*x - 8)", "integrand_latex": "2 \\cos{\\left(15 x - 8 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(15 x - 8 \\right)} \\, dx", "reference_antiderivative": "2*sin(15*x - 8)/15", "category": "trigonometric", "variable": "x"}
{"id": "atom-0253", "stage": "atomic", "k": 1, "integrand": "-5*tan(4*x - 2)", "integrand_latex": "- 5 \\tan{\\left(4 x - 2 \\right)}", "integrand_latex_integral": "\\int - 5 \\tan{\\left(4 x - 2 \\right)} \\, dx", "reference_antiderivative": "-5*log(tan(4*x - 2)**2 + 1)/8", "category": "trigonometric", "variable": "x"}
{"id": "atom-0254", "stage": "atomic", "k": 1, "integrand": "-sin(7*x + 9)", "integrand_latex": "- \\sin{\\left(7 x + 9 \\right)}", "integrand_latex_integral": "\\int - \\sin{\\left(7 x + 9 \\right)} \\, dx", "reference_antiderivative": "cos(7*x + 9)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0255", "stage": "atomic", "k": 1, "integrand": "-2*sin(13*x - 6)", "integrand_latex": "- 2 \\sin{\\left(13 x - 6 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(13 x - 6 \\right)} \\, dx", "reference_antiderivative": "2*cos(13*x - 6)/13", "category": "trigonometric", "variable": "x"}
{"id": "atom-0256", "stage": "atomic", "k": 1, "integrand": "4*cos(15*x + 14)", "integrand_latex": "4 \\cos{\\left(15 x + 14 \\right)}", "integrand_latex_integral": "\\int 4 \\cos{\\left(15 x + 14 \\right)} \\, dx", "reference_antiderivative": "4*sin(15*x + 14)/15", "category": "trigonometric", "variable": "x"}
{"id": "atom-0257", "stage": "atomic", "k": 1, "integrand": "-3*sin(10*x + 3)", "integrand_latex": "- 3 \\sin{\\left(10 x + 3 \\right)}", "integrand_latex_integral": "\\int - 3 \\sin{\\left(10 x + 3 \\right)} \\, dx", "reference_antiderivative": "3*cos(10*x + 3)/10", "category": "trigonometric", "variable": "x"}
{"id": "atom-0258", "stage": "atomic", "k": 1, "integrand": "-3*sin(9*x - 3)", "integrand_latex": "- 3 \\sin{\\left(9 x - 3 \\right)}", "integrand_latex_integral": "\\int - 3 \\sin{\\left(9 x - 3 \\right)} \\, dx", "reference_antiderivative": "cos(9*x - 3)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0259", "stage": "atomic", "k": 1, "integrand": "2*sin(5*x - 9)", "integrand_latex": "2 \\sin{\\left(5 x - 9 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(5 x - 9 \\right)} \\, dx", "reference_antiderivative": "-2*cos(5*x - 9)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0260", "stage": "atomic", "k": 1, "integrand": "-4*sin(15*x + 7)", "integrand_latex": "- 4 \\sin{\\left(15 x + 7 \\right)}", "integrand_latex_integral": "\\int - 4 \\sin{\\left(15 x + 7 \\right)} \\, dx", "reference_antiderivative": "4*cos(15*x + 7)/15", "category": "trigonometric", "variable": "x"}
{"id": "atom-0261", "stage": "atomic", "k": 1, "integrand": "-3*sin(7*x - 10)", "integrand_latex": "- 3 \\sin{\\left(7 x - 10 \\right)}", "integrand_latex_integral": "\\int - 3 \\sin{\\left(7 x - 10 \\right)} \\, dx", "reference_antiderivative": "3*cos(7*x - 10)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0262", "stage": "atomic", "k": 1, "integrand": "-5*cos(11*x + 15)", "integrand_latex": "- 5 \\cos{\\left(11 x + 15 \\right)}", "integrand_latex_integral": "\\int - 5 \\cos{\\left(11 x + 15 \\right)} \\, dx", "reference_antiderivative": "-5*sin(11*x + 15)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0263", "stage": "atomic", "k": 1, "integrand": "-2*sin(3*x - 5)", "integrand_latex": "- 2 \\sin{\\left(3 x - 5 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(3 x - 5 \\right)} \\, dx", "reference_antiderivative": "2*cos(3*x - 5)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0264", "stage": "atomic", "k": 1, "integrand": "-5*cos(11*x - 8)", "integrand_latex": "- 5 \\cos{\\left(11 x - 8 \\right)}", "integrand_latex_integral": "\\int - 5 \\cos{\\left(11 x - 8 \\right)} \\, dx", "reference_antiderivative": "-5*sin(11*x - 8)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0265", "stage": "atomic", "k": 1, "integrand": "-4*cos(x - 9)", "integrand_latex": "- 4 \\cos{\\left(x - 9 \\right)}", "integrand_latex_integral": "\\int - 4 \\cos{\\left(x - 9 \\right)} \\, dx", "reference_antiderivative": "-4*sin(x - 9)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0266", "stage": "atomic", "k": 1, "integrand": "4*sin(x - 1)", "integrand_latex": "4 \\sin{\\left(x - 1 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(x - 1 \\right)} \\, dx", "reference_antiderivative": "-4*cos(x - 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0267", "stage": "atomic", "k": 1, "integrand": "-5*tan(8*x + 10)", "integrand_latex": "- 5 \\tan{\\left(8 x + 10 \\right)}", "integrand_latex_integral": "\\int - 5 \\tan{\\left(8 x + 10 \\right)} \\, dx", "reference_antiderivative": "-5*log(tan(8*x + 10)**2 + 1)/16", "category": "trigonometric", "variable": "x"}
{"id": "atom-0268", "stage": "atomic", "k": 1, "integrand": "2*sin(5*x + 15)", "integrand_latex": "2 \\sin{\\left(5 x + 15 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(5 x + 15 \\right)} \\, dx", "reference_antiderivative": "-2*cos(5*x + 15)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0269", "stage": "atomic", "k": 1, "integrand": "2*cos(12*x - 3)", "integrand_latex": "2 \\cos{\\left(12 x - 3 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(12 x - 3 \\right)} \\, dx", "reference_antiderivative": "sin(12*x - 3)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0270", "stage": "atomic", "k": 1, "integrand": "4*sin(5*x - 4)", "integrand_latex": "4 \\sin{\\left(5 x - 4 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(5 x - 4 \\right)} \\, dx", "reference_antiderivative": "-4*cos(5*x - 4)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0271", "stage": "atomic", "k": 1, "integrand": "-tan(4*x + 5)", "integrand_latex": "- \\tan{\\left(4 x + 5 \\right)}", "integrand_latex_integral": "\\int - \\tan{\\left(4 x + 5 \\right)} \\, dx", "reference_antiderivative": "-log(tan(4*x + 5)**2 + 1)/8", "category": "trigonometric", "variable": "x"}
{"id": "atom-0272", "stage": "atomic", "k": 1, "integrand": "cos(4*x + 1)", "integrand_latex": "\\cos{\\left(4 x + 1 \\right)}", "integrand_latex_integral": "\\int \\cos{\\left(4 x + 1 \\right)} \\, dx", "reference_antiderivative": "sin(4*x + 1)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0273", "stage": "atomic", "k": 1, "integrand": "-4*tan(2*x + 12)", "integrand_latex": "- 4 \\tan{\\left(2 x + 12 \\right)}", "integrand_latex_integral": "\\int - 4 \\tan{\\left(2 x + 12 \\right)} \\, dx", "reference_antiderivative": "-log(tan(2*x + 12)**2 + 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0274", "stage": "atomic", "k": 1, "integrand": "5*tan(5*x + 13)", "integrand_latex": "5 \\tan{\\left(5 x + 13 \\right)}", "integrand_latex_integral": "\\int 5 \\tan{\\left(5 x + 13 \\right)} \\, dx", "reference_antiderivative": "log(tan(5*x + 13)**2 + 1)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0275", "stage": "atomic", "k": 1, "integrand": "2*sin(2*x + 1)", "integrand_latex": "2 \\sin{\\left(2 x + 1 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(2 x + 1 \\right)} \\, dx", "reference_antiderivative": "-cos(2*x + 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0276", "stage": "atomic", "k": 1, "integrand": "-2*tan(3*x + 2)", "integrand_latex": "- 2 \\tan{\\left(3 x + 2 \\right)}", "integrand_latex_integral": "\\int - 2 \\tan{\\left(3 x + 2 \\right)} \\, dx", "reference_antiderivative": "-log(tan(3*x + 2)**2 + 1)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0277", "stage": "atomic", "k": 1, "integrand": "cos(5*x - 6)", "integrand_latex": "\\cos{\\left(5 x - 6 \\right)}", "integrand_latex_integral": "\\int \\cos{\\left(5 x - 6 \\right)} \\, dx", "reference_antiderivative": "sin(5*x - 6)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0278", "stage": "atomic", "k": 1, "integrand": "-3*cos(6*x + 14)", "integrand_latex": "- 3 \\cos{\\left(6 x + 14 \\right)}", "integrand_latex_integral": "\\int - 3 \\cos{\\left(6 x + 14 \\right)} \\, dx", "reference_antiderivative": "-sin(6*x + 14)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0279", "stage": "atomic", "k": 1, "integrand": "4*sin(13*x + 2)", "integrand_latex": "4 \\sin{\\left(13 x + 2 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(13 x + 2 \\right)} \\, dx", "reference_antiderivative": "-4*cos(13*x + 2)/13", "category": "trigonometric", "variable": "x"}
{"id": "atom-0280", "stage": "atomic", "k": 1, "integrand": "-3*tan(2*x - 14)", "integrand_latex": "- 3 \\tan{\\left(2 x - 14 \\right)}", "integrand_latex_integral": "\\int - 3 \\tan{\\left(2 x - 14 \\right)} \\, dx", "reference_antiderivative": "-3*log(tan(2*x - 14)**2 + 1)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0281", "stage": "atomic", "k": 1, "integrand": "-3*sin(5*x - 6)", "integrand_latex": "- 3 \\sin{\\left(5 x - 6 \\right)}", "integrand_latex_integral": "\\int - 3 \\sin{\\left(5 x - 6 \\right)} \\, dx", "reference_antiderivative": "3*cos(5*x - 6)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0282", "stage": "atomic", "k": 1, "integrand": "5*cos(15*x + 9)", "integrand_latex": "5 \\cos{\\left(15 x + 9 \\right)}", "integrand_latex_integral": "\\int 5 \\cos{\\left(15 x + 9 \\right)} \\, dx", "reference_antiderivative": "sin(15*x + 9)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0283", "stage": "atomic", "k": 1, "integrand": "-5*tan(15*x - 6)", "integrand_latex": "- 5 \\tan{\\left(15 x - 6 \\right)}", "integrand_latex_integral": "\\int - 5 \\tan{\\left(15 x - 6 \\right)} \\, dx", "reference_antiderivative": "-log(tan(15*x - 6)**2 + 1)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0284", "stage": "atomic", "k": 1, "integrand": "-4*sin(3*x + 1)", "integrand_latex": "- 4 \\sin{\\left(3 x + 1 \\right)}", "integrand_latex_integral": "\\int - 4 \\sin{\\left(3 x + 1 \\right)} \\, dx", "reference_antiderivative": "4*cos(3*x + 1)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0285", "stage": "atomic", "k": 1, "integrand": "-2*sin(8*x - 12)", "integrand_latex": "- 2 \\sin{\\left(8 x - 12 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(8 x - 12 \\right)} \\, dx", "reference_antiderivative": "cos(8*x - 12)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0286", "stage": "atomic", "k": 1, "integrand": "3*cos(4*x + 12)", "integrand_latex": "3 \\cos{\\left(4 x + 12 \\right)}", "integrand_latex_integral": "\\int 3 \\cos{\\left(4 x + 12 \\right)} \\, dx", "reference_antiderivative": "3*sin(4*x + 12)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0287", "stage": "atomic", "k": 1, "integrand": "tan(12*x + 2)", "integrand_latex": "\\tan{\\left(12 x + 2 \\right)}", "integrand_latex_integral": "\\int \\tan{\\left(12 x + 2 \\right)} \\, dx", "reference_antiderivative": "log(tan(12*x + 2)**2 + 1)/24", "category": "trigonometric", "variable": "x"}
{"id": "atom-0288", "stage": "atomic", "k": 1, "integrand": "5*tan(2*x - 15)", "integrand_latex": "5 \\tan{\\left(2 x - 15 \\right)}", "integrand_latex_integral": "\\int 5 \\tan{\\left(2 x - 15 \\right)} \\, dx", "reference_antiderivative": "5*log(tan(2*x - 15)**2 + 1)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0289", "stage": "atomic", "k": 1, "integrand": "-cos(15*x + 10)", "integrand_latex": "- \\cos{\\left(15 x + 10 \\right)}", "integrand_latex_integral": "\\int - \\cos{\\left(15 x + 10 \\right)} \\, dx", "reference_antiderivative": "-sin(15*x + 10)/15", "category": "trigonometric", "variable": "x"}
{"id": "atom-0290", "stage": "atomic", "k": 1, "integrand": "-cos(14*x - 5)", "integrand_latex": "- \\cos{\\left(14 x - 5 \\right)}", "integrand_latex_integral": "\\int - \\cos{\\left(14 x - 5 \\right)} \\, dx", "reference_antiderivative": "-sin(14*x - 5)/14", "category": "trigonometric", "variable": "x"}
{"id": "atom-0291", "stage": "atomic", "k": 1, "integrand": "-3*cos(3*x + 6)", "integrand_latex": "- 3 \\cos{\\left(3 x + 6 \\right)}", "integrand_latex_integral": "\\int - 3 \\cos{\\left(3 x + 6 \\right)} \\, dx", "reference_antiderivative": "-sin(3*x + 6)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0292", "stage": "atomic", "k": 1, "integrand": "-5*tan(15*x + 13)", "integrand_latex": "- 5 \\tan{\\left(15 x + 13 \\right)}", "integrand_latex_integral": "\\int - 5 \\tan{\\left(15 x + 13 \\right)} \\, dx", "reference_antiderivative": "-log(tan(15*x + 13)**2 + 1)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0293", "stage": "atomic", "k": 1, "integrand": "cos(2*x + 1)", "integrand_latex": "\\cos{\\left(2 x + 1 \\right)}", "integrand_latex_integral": "\\int \\cos{\\left(2 x + 1 \\right)} \\, dx", "reference_antiderivative": "sin(2*x + 1)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0294", "stage": "atomic", "k": 1, "integrand": "-tan(8*x - 5)", "integrand_latex": "- \\tan{\\left(8 x - 5 \\right)}", "integrand_latex_integral": "\\int - \\tan{\\left(8 x - 5 \\right)} \\, dx", "reference_antiderivative": "-log(tan(8*x - 5)**2 + 1)/16", "category": "trigonometric", "variable": "x"}
{"id": "atom-0295", "stage": "atomic", "k": 1, "integrand": "5*tan(11*x + 10)", "integrand_latex": "5 \\tan{\\left(11 x + 10 \\right)}", "integrand_latex_integral": "\\int 5 \\tan{\\left(11 x + 10 \\right)} \\, dx", "reference_antiderivative": "5*log(tan(11*x + 10)**2 + 1)/22", "category": "trigonometric", "variable": "x"}
{"id": "atom-0296", "stage": "atomic", "k": 1, "integrand": "4*tan(7*x + 1)", "integrand_latex": "4 \\tan{\\left(7 x + 1 \\right)}", "integrand_latex_integral": "\\int 4 \\tan{\\left(7 x + 1 \\right)} \\, dx", "reference_antiderivative": "2*log(tan(7*x + 1)**2 + 1)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0297", "stage": "atomic", "k": 1, "integrand": "4*cos(x + 2)", "integrand_latex": "4 \\cos{\\left(x + 2 \\right)}", "integrand_latex_integral": "\\int 4 \\cos{\\left(x + 2 \\right)} \\, dx", "reference_antiderivative": "4*sin(x + 2)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0298", "stage": "atomic", "k": 1, "integrand": "3*cos(12*x + 4)", "integrand_latex": "3 \\cos{\\left(12 x + 4 \\right)}", "integrand_latex_integral": "\\int 3 \\cos{\\left(12 x + 4 \\right)} \\, dx", "reference_antiderivative": "sin(12*x + 4)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0299", "stage": "atomic", "k": 1, "integrand": "5*cos(6*x + 3)", "integrand_latex": "5 \\cos{\\left(6 x + 3 \\right)}", "integrand_latex_integral": "\\int 5 \\cos{\\left(6 x + 3 \\right)} \\, dx", "reference_antiderivative": "5*sin(6*x + 3)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0300", "stage": "atomic", "k": 1, "integrand": "-cos(14*x + 8)", "integrand_latex": "- \\cos{\\left(14 x + 8 \\right)}", "integrand_latex_integral": "\\int - \\cos{\\left(14 x + 8 \\right)} \\, dx", "reference_antiderivative": "-sin(14*x + 8)/14", "category": "trigonometric", "variable": "x"}
{"id": "atom-0301", "stage": "atomic", "k": 1, "integrand": "-5*cos(15*x + 9)", "integrand_latex": "- 5 \\cos{\\left(15 x + 9 \\right)}", "integrand_latex_integral": "\\int - 5 \\cos{\\left(15 x + 9 \\right)} \\, dx", "reference_antiderivative": "-sin(15*x + 9)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0302", "stage": "atomic", "k": 1, "integrand": "-3*cos(9*x - 7)", "integrand_latex": "- 3 \\cos{\\left(9 x - 7 \\right)}", "integrand_latex_integral": "\\int - 3 \\cos{\\left(9 x - 7 \\right)} \\, dx", "reference_antiderivative": "-sin(9*x - 7)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0303", "stage": "atomic", "k": 1, "integrand": "-5*sin(8*x - 2)", "integrand_latex": "- 5 \\sin{\\left(8 x - 2 \\right)}", "integrand_latex_integral": "\\int - 5 \\sin{\\left(8 x - 2 \\right)} \\, dx", "reference_antiderivative": "5*cos(8*x - 2)/8", "category": "trigonometric", "variable": "x"}
{"id": "atom-0304", "stage": "atomic", "k": 1, "integrand": "3*tan(7*x - 8)", "integrand_latex": "3 \\tan{\\left(7 x - 8 \\right)}", "integrand_latex_integral": "\\int 3 \\tan{\\left(7 x - 8 \\right)} \\, dx", "reference_antiderivative": "3*log(tan(7*x - 8)**2 + 1)/14", "category": "trigonometric", "variable": "x"}
{"id": "atom-0305", "stage": "atomic", "k": 1, "integrand": "5*sin(10*x - 4)", "integrand_latex": "5 \\sin{\\left(10 x - 4 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(10 x - 4 \\right)} \\, dx", "reference_antiderivative": "-cos(10*x - 4)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0306", "stage": "atomic", "k": 1, "integrand": "-5*cos(2*x + 15)", "integrand_latex": "- 5 \\cos{\\left(2 x + 15 \\right)}", "integrand_latex_integral": "\\int - 5 \\cos{\\left(2 x + 15 \\right)} \\, dx", "reference_antiderivative": "-5*sin(2*x + 15)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0307", "stage": "atomic", "k": 1, "integrand": "4*cos(2*x - 3)", "integrand_latex": "4 \\cos{\\left(2 x - 3 \\right)}", "integrand_latex_integral": "\\int 4 \\cos{\\left(2 x - 3 \\right)} \\, dx", "reference_antiderivative": "2*sin(2*x - 3)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0308", "stage": "atomic", "k": 1, "integrand": "cos(6*x + 12)", "integrand_latex": "\\cos{\\left(6 x + 12 \\right)}", "integrand_latex_integral": "\\int \\cos{\\left(6 x + 12 \\right)} \\, dx", "reference_antiderivative": "sin(6*x + 12)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0309", "stage": "atomic", "k": 1, "integrand": "-3*tan(10*x + 15)", "integrand_latex": "- 3 \\tan{\\left(10 x + 15 \\right)}", "integrand_latex_integral": "\\int - 3 \\tan{\\left(10 x + 15 \\right)} \\, dx", "reference_antiderivative": "-3*log(tan(10*x + 15)**2 + 1)/20", "category": "trigonometric", "variable": "x"}
{"id": "atom-0310", "stage": "atomic", "k": 1, "integrand": "4*sin(2*x - 12)", "integrand_latex": "4 \\sin{\\left(2 x - 12 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(2 x - 12 \\right)} \\, dx", "reference_antiderivative": "-2*cos(2*x - 12)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0311", "stage": "atomic", "k": 1, "integrand": "-4*sin(3*x - 1)", "integrand_latex": "- 4 \\sin{\\left(3 x - 1 \\right)}", "integrand_latex_integral": "\\int - 4 \\sin{\\left(3 x - 1 \\right)} \\, dx", "reference_antiderivative": "4*cos(3*x - 1)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0312", "stage": "atomic", "k": 1, "integrand": "-sin(8*x - 5)", "integrand_latex": "- \\sin{\\left(8 x - 5 \\right)}", "integrand_latex_integral": "\\int - \\sin{\\left(8 x - 5 \\right)} \\, dx", "reference_antiderivative": "cos(8*x - 5)/8", "category": "trigonometric", "variable": "x"}
{"id": "atom-0313", "stage": "atomic", "k": 1, "integrand": "3*tan(13*x - 1)", "integrand_latex": "3 \\tan{\\left(13 x - 1 \\right)}", "integrand_latex_integral": "\\int 3 \\tan{\\left(13 x - 1 \\right)} \\, dx", "reference_antiderivative": "3*log(tan(13*x - 1)**2 + 1)/26", "category": "trigonometric", "variable": "x"}
{"id": "atom-0314", "stage": "atomic", "k": 1, "integrand": "3*cos(9*x - 13)", "integrand_latex": "3 \\cos{\\left(9 x - 13 \\right)}", "integrand_latex_integral": "\\int 3 \\cos{\\left(9 x - 13 \\right)} \\, dx", "reference_antiderivative": "sin(9*x - 13)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0315", "stage": "atomic", "k": 1, "integrand": "5*sin(11*x - 11)", "integrand_latex": "5 \\sin{\\left(11 x - 11 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(11 x - 11 \\right)} \\, dx", "reference_antiderivative": "-5*cos(11*x - 11)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0316", "stage": "atomic", "k": 1, "integrand": "tan(9*x + 10)", "integrand_latex": "\\tan{\\left(9 x + 10 \\right)}", "integrand_latex_integral": "\\int \\tan{\\left(9 x + 10 \\right)} \\, dx", "reference_antiderivative": "log(tan(9*x + 10)**2 + 1)/18", "category": "trigonometric", "variable": "x"}
{"id": "atom-0317", "stage": "atomic", "k": 1, "integrand": "-5*tan(13*x + 10)", "integrand_latex": "- 5 \\tan{\\left(13 x + 10 \\right)}", "integrand_latex_integral": "\\int - 5 \\tan{\\left(13 x + 10 \\right)} \\, dx", "reference_antiderivative": "-5*log(tan(13*x + 10)**2 + 1)/26", "category": "trigonometric", "variable": "x"}
{"id": "atom-0318", "stage": "atomic", "k": 1, "integrand": "4*cos(9*x + 3)", "integrand_latex": "4 \\cos{\\left(9 x + 3 \\right)}", "integrand_latex_integral": "\\int 4 \\cos{\\left(9 x + 3 \\right)} \\, dx", "reference_antiderivative": "4*sin(9*x + 3)/9", "category": "trigonometric", "variable": "x"}
{"id": "atom-0319", "stage": "atomic", "k": 1, "integrand": "4*tan(5*x + 5)", "integrand_latex": "4 \\tan{\\left(5 x + 5 \\right)}", "integrand_latex_integral": "\\int 4 \\tan{\\left(5 x + 5 \\right)} \\, dx", "reference_antiderivative": "2*log(tan(5*x + 5)**2 + 1)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0320", "stage": "atomic", "k": 1, "integrand": "5*cos(5*x + 11)", "integrand_latex": "5 \\cos{\\left(5 x + 11 \\right)}", "integrand_latex_integral": "\\int 5 \\cos{\\left(5 x + 11 \\right)} \\, dx", "reference_antiderivative": "sin(5*x + 11)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0321", "stage": "atomic", "k": 1, "integrand": "2*cos(5*x - 6)", "integrand_latex": "2 \\cos{\\left(5 x - 6 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(5 x - 6 \\right)} \\, dx", "reference_antiderivative": "2*sin(5*x - 6)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0322", "stage": "atomic", "k": 1, "integrand": "3*cos(13*x + 6)", "integrand_latex": "3 \\cos{\\left(13 x + 6 \\right)}", "integrand_latex_integral": "\\int 3 \\cos{\\left(13 x + 6 \\right)} \\, dx", "reference_antiderivative": "3*sin(13*x + 6)/13", "category": "trigonometric", "variable": "x"}
{"id": "atom-0323", "stage": "atomic", "k": 1, "integrand": "-5*cos(4*x - 11)", "integrand_latex": "- 5 \\cos{\\left(4 x - 11 \\right)}", "integrand_latex_integral": "\\int - 5 \\cos{\\left(4 x - 11 \\right)} \\, dx", "reference_antiderivative": "-5*sin(4*x - 11)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0324", "stage": "atomic", "k": 1, "integrand": "-4*tan(4*x + 4)", "integrand_latex": "- 4 \\tan{\\left(4 x + 4 \\right)}", "integrand_latex_integral": "\\int - 4 \\tan{\\left(4 x + 4 \\right)} \\, dx", "reference_antiderivative": "-log(tan(4*x + 4)**2 + 1)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0325", "stage": "atomic", "k": 1, "integrand": "4*tan(2*x + 15)", "integrand_latex": "4 \\tan{\\left(2 x + 15 \\right)}", "integrand_latex_integral": "\\int 4 \\tan{\\left(2 x + 15 \\right)} \\, dx", "reference_antiderivative": "log(tan(2*x + 15)**2 + 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0326", "stage": "atomic", "k": 1, "integrand": "2*tan(14*x + 10)", "integrand_latex": "2 \\tan{\\left(14 x + 10 \\right)}", "integrand_latex_integral": "\\int 2 \\tan{\\left(14 x + 10 \\right)} \\, dx", "reference_antiderivative": "log(tan(14*x + 10)**2 + 1)/14", "category": "trigonometric", "variable": "x"}
{"id": "atom-0327", "stage": "atomic", "k": 1, "integrand": "4*sin(x - 11)", "integrand_latex": "4 \\sin{\\left(x - 11 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(x - 11 \\right)} \\, dx", "reference_antiderivative": "-4*cos(x - 11)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0328", "stage": "atomic", "k": 1, "integrand": "-4*sin(x + 5)", "integrand_latex": "- 4 \\sin{\\left(x + 5 \\right)}", "integrand_latex_integral": "\\int - 4 \\sin{\\left(x + 5 \\right)} \\, dx", "reference_antiderivative": "4*cos(x + 5)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0329", "stage": "atomic", "k": 1, "integrand": "-2*tan(x - 1)", "integrand_latex": "- 2 \\tan{\\left(x - 1 \\right)}", "integrand_latex_integral": "\\int - 2 \\tan{\\left(x - 1 \\right)} \\, dx", "reference_antiderivative": "-log(tan(x - 1)**2 + 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0330", "stage": "atomic", "k": 1, "integrand": "-cos(3*x + 2)", "integrand_latex": "- \\cos{\\left(3 x + 2 \\right)}", "integrand_latex_integral": "\\int - \\cos{\\left(3 x + 2 \\right)} \\, dx", "reference_antiderivative": "-sin(3*x + 2)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0331", "stage": "atomic", "k": 1, "integrand": "-5*tan(10*x + 5)", "integrand_latex": "- 5 \\tan{\\left(10 x + 5 \\right)}", "integrand_latex_integral": "\\int - 5 \\tan{\\left(10 x + 5 \\right)} \\, dx", "reference_antiderivative": "-log(tan(10*x + 5)**2 + 1)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0332", "stage": "atomic", "k": 1, "integrand": "-4*cos(2*x + 6)", "integrand_latex": "- 4 \\cos{\\left(2 x + 6 \\right)}", "integrand_latex_integral": "\\int - 4 \\cos{\\left(2 x + 6 \\right)} \\, dx", "reference_antiderivative": "-2*sin(2*x + 6)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0333", "stage": "atomic", "k": 1, "integrand": "5*tan(15*x + 14)", "integrand_latex": "5 \\tan{\\left(15 x + 14 \\right)}", "integrand_latex_integral": "\\int 5 \\tan{\\left(15 x + 14 \\right)} \\, dx", "reference_antiderivative": "log(tan(15*x + 14)**2 + 1)/6", "category": "trigonometric", "variable": "x"}
{"id": "atom-0334", "stage": "atomic", "k": 1, "integrand": "-4*sin(3*x + 6)", "integrand_latex": "- 4 \\sin{\\left(3 x + 6 \\right)}", "integrand_latex_integral": "\\int - 4 \\sin{\\left(3 x + 6 \\right)} \\, dx", "reference_antiderivative": "4*cos(3*x + 6)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0335", "stage": "atomic", "k": 1, "integrand": "-tan(15*x + 5)", "integrand_latex": "- \\tan{\\left(15 x + 5 \\right)}", "integrand_latex_integral": "\\int - \\tan{\\left(15 x + 5 \\right)} \\, dx", "reference_antiderivative": "-log(tan(15*x + 5)**2 + 1)/30", "category": "trigonometric", "variable": "x"}
{"id": "atom-0336", "stage": "atomic", "k": 1, "integrand": "-3*sin(4*x + 7)", "integrand_latex": "- 3 \\sin{\\left(4 x + 7 \\right)}", "integrand_latex_integral": "\\int - 3 \\sin{\\left(4 x + 7 \\right)} \\, dx", "reference_antiderivative": "3*cos(4*x + 7)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0337", "stage": "atomic", "k": 1, "integrand": "cos(5*x + 10)", "integrand_latex": "\\cos{\\left(5 x + 10 \\right)}", "integrand_latex_integral": "\\int \\cos{\\left(5 x + 10 \\right)} \\, dx", "reference_antiderivative": "sin(5*x + 10)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0338", "stage": "atomic", "k": 1, "integrand": "5*tan(7*x + 11)", "integrand_latex": "5 \\tan{\\left(7 x + 11 \\right)}", "integrand_latex_integral": "\\int 5 \\tan{\\left(7 x + 11 \\right)} \\, dx", "reference_antiderivative": "5*log(tan(7*x + 11)**2 + 1)/14", "category": "trigonometric", "variable": "x"}
{"id": "atom-0339", "stage": "atomic", "k": 1, "integrand": "-3*tan(13*x - 5)", "integrand_latex": "- 3 \\tan{\\left(13 x - 5 \\right)}", "integrand_latex_integral": "\\int - 3 \\tan{\\left(13 x - 5 \\right)} \\, dx", "reference_antiderivative": "-3*log(tan(13*x - 5)**2 + 1)/26", "category": "trigonometric", "variable": "x"}
{"id": "atom-0340", "stage": "atomic", "k": 1, "integrand": "5*sin(4*x + 6)", "integrand_latex": "5 \\sin{\\left(4 x + 6 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(4 x + 6 \\right)} \\, dx", "reference_antiderivative": "-5*cos(4*x + 6)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0341", "stage": "atomic", "k": 1, "integrand": "-2*sin(9*x + 8)", "integrand_latex": "- 2 \\sin{\\left(9 x + 8 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(9 x + 8 \\right)} \\, dx", "reference_antiderivative": "2*cos(9*x + 8)/9", "category": "trigonometric", "variable": "x"}
{"id": "atom-0342", "stage": "atomic", "k": 1, "integrand": "-sin(12*x + 10)", "integrand_latex": "- \\sin{\\left(12 x + 10 \\right)}", "integrand_latex_integral": "\\int - \\sin{\\left(12 x + 10 \\right)} \\, dx", "reference_antiderivative": "cos(12*x + 10)/12", "category": "trigonometric", "variable": "x"}
{"id": "atom-0343", "stage": "atomic", "k": 1, "integrand": "3*tan(11*x + 8)", "integrand_latex": "3 \\tan{\\left(11 x + 8 \\right)}", "integrand_latex_integral": "\\int 3 \\tan{\\left(11 x + 8 \\right)} \\, dx", "reference_antiderivative": "3*log(tan(11*x + 8)**2 + 1)/22", "category": "trigonometric", "variable": "x"}
{"id": "atom-0344", "stage": "atomic", "k": 1, "integrand": "4*cos(11*x - 4)", "integrand_latex": "4 \\cos{\\left(11 x - 4 \\right)}", "integrand_latex_integral": "\\int 4 \\cos{\\left(11 x - 4 \\right)} \\, dx", "reference_antiderivative": "4*sin(11*x - 4)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0345", "stage": "atomic", "k": 1, "integrand": "-3*tan(11*x + 7)", "integrand_latex": "- 3 \\tan{\\left(11 x + 7 \\right)}", "integrand_latex_integral": "\\int - 3 \\tan{\\left(11 x + 7 \\right)} \\, dx", "reference_antiderivative": "-3*log(tan(11*x + 7)**2 + 1)/22", "category": "trigonometric", "variable": "x"}
{"id": "atom-0346", "stage": "atomic", "k": 1, "integrand": "-3*sin(8*x - 1)", "integrand_latex": "- 3 \\sin{\\left(8 x - 1 \\right)}", "integrand_latex_integral": "\\int - 3 \\sin{\\left(8 x - 1 \\right)} \\, dx", "reference_antiderivative": "3*cos(8*x - 1)/8", "category": "trigonometric", "variable": "x"}
{"id": "atom-0347", "stage": "atomic", "k": 1, "integrand": "5*cos(8*x - 8)", "integrand_latex": "5 \\cos{\\left(8 x - 8 \\right)}", "integrand_latex_integral": "\\int 5 \\cos{\\left(8 x - 8 \\right)} \\, dx", "reference_antiderivative": "5*sin(8*x - 8)/8", "category": "trigonometric", "variable": "x"}
{"id": "atom-0348", "stage": "atomic", "k": 1, "integrand": "-2*sin(8*x - 2)", "integrand_latex": "- 2 \\sin{\\left(8 x - 2 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(8 x - 2 \\right)} \\, dx", "reference_antiderivative": "cos(8*x - 2)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0349", "stage": "atomic", "k": 1, "integrand": "2*sin(13*x + 11)", "integrand_latex": "2 \\sin{\\left(13 x + 11 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(13 x + 11 \\right)} \\, dx", "reference_antiderivative": "-2*cos(13*x + 11)/13", "category": "trigonometric", "variable": "x"}
{"id": "atom-0350", "stage": "atomic", "k": 1, "integrand": "4*cos(x + 1)", "integrand_latex": "4 \\cos{\\left(x + 1 \\right)}", "integrand_latex_integral": "\\int 4 \\cos{\\left(x + 1 \\right)} \\, dx", "reference_antiderivative": "4*sin(x + 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0351", "stage": "atomic", "k": 1, "integrand": "3*sin(x - 2)", "integrand_latex": "3 \\sin{\\left(x - 2 \\right)}", "integrand_latex_integral": "\\int 3 \\sin{\\left(x - 2 \\right)} \\, dx", "reference_antiderivative": "-3*cos(x - 2)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0352", "stage": "atomic", "k": 1, "integrand": "4*cos(11*x - 12)", "integrand_latex": "4 \\cos{\\left(11 x - 12 \\right)}", "integrand_latex_integral": "\\int 4 \\cos{\\left(11 x - 12 \\right)} \\, dx", "reference_antiderivative": "4*sin(11*x - 12)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0353", "stage": "atomic", "k": 1, "integrand": "2*tan(12*x - 4)", "integrand_latex": "2 \\tan{\\left(12 x - 4 \\right)}", "integrand_latex_integral": "\\int 2 \\tan{\\left(12 x - 4 \\right)} \\, dx", "reference_antiderivative": "log(tan(12*x - 4)**2 + 1)/12", "category": "trigonometric", "variable": "x"}
{"id": "atom-0354", "stage": "atomic", "k": 1, "integrand": "3*cos(12*x - 12)", "integrand_latex": "3 \\cos{\\left(12 x - 12 \\right)}", "integrand_latex_integral": "\\int 3 \\cos{\\left(12 x - 12 \\right)} \\, dx", "reference_antiderivative": "sin(12*x - 12)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0355", "stage": "atomic", "k": 1, "integrand": "3*tan(7*x + 1)", "integrand_latex": "3 \\tan{\\left(7 x + 1 \\right)}", "integrand_latex_integral": "\\int 3 \\tan{\\left(7 x + 1 \\right)} \\, dx", "reference_antiderivative": "3*log(tan(7*x + 1)**2 + 1)/14", "category": "trigonometric", "variable": "x"}
{"id": "atom-0356", "stage": "atomic", "k": 1, "integrand": "-sin(13*x - 15)", "integrand_latex": "- \\sin{\\left(13 x - 15 \\right)}", "integrand_latex_integral": "\\int - \\sin{\\left(13 x - 15 \\right)} \\, dx", "reference_antiderivative": "cos(13*x - 15)/13", "category": "trigonometric", "variable": "x"}
{"id": "atom-0357", "stage": "atomic", "k": 1, "integrand": "-5*cos(2*x + 14)", "integrand_latex": "- 5 \\cos{\\left(2 x + 14 \\right)}", "integrand_latex_integral": "\\int - 5 \\cos{\\left(2 x + 14 \\right)} \\, dx", "reference_antiderivative": "-5*sin(2*x + 14)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0358", "stage": "atomic", "k": 1, "integrand": "-2*cos(3*x + 13)", "integrand_latex": "- 2 \\cos{\\left(3 x + 13 \\right)}", "integrand_latex_integral": "\\int - 2 \\cos{\\left(3 x + 13 \\right)} \\, dx", "reference_antiderivative": "-2*sin(3*x + 13)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0359", "stage": "atomic", "k": 1, "integrand": "-4*tan(11*x + 7)", "integrand_latex": "- 4 \\tan{\\left(11 x + 7 \\right)}", "integrand_latex_integral": "\\int - 4 \\tan{\\left(11 x + 7 \\right)} \\, dx", "reference_antiderivative": "-2*log(tan(11*x + 7)**2 + 1)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0360", "stage": "atomic", "k": 1, "integrand": "-3*cos(11*x + 14)", "integrand_latex": "- 3 \\cos{\\left(11 x + 14 \\right)}", "integrand_latex_integral": "\\int - 3 \\cos{\\left(11 x + 14 \\right)} \\, dx", "reference_antiderivative": "-3*sin(11*x + 14)/11", "category": "trigonometric", "variable": "x"}
{"id": "atom-0361", "stage": "atomic", "k": 1, "integrand": "2*sin(7*x + 11)", "integrand_latex": "2 \\sin{\\left(7 x + 11 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(7 x + 11 \\right)} \\, dx", "reference_antiderivative": "-2*cos(7*x + 11)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0362", "stage": "atomic", "k": 1, "integrand": "-2*sin(x - 4)", "integrand_latex": "- 2 \\sin{\\left(x - 4 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(x - 4 \\right)} \\, dx", "reference_antiderivative": "2*cos(x - 4)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0363", "stage": "atomic", "k": 1, "integrand": "5*sin(7*x + 9)", "integrand_latex": "5 \\sin{\\left(7 x + 9 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(7 x + 9 \\right)} \\, dx", "reference_antiderivative": "-5*cos(7*x + 9)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0364", "stage": "atomic", "k": 1, "integrand": "4*sin(x - 2)", "integrand_latex": "4 \\sin{\\left(x - 2 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(x - 2 \\right)} \\, dx", "reference_antiderivative": "-4*cos(x - 2)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0365", "stage": "atomic", "k": 1, "integrand": "2*sin(6*x + 12)", "integrand_latex": "2 \\sin{\\left(6 x + 12 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(6 x + 12 \\right)} \\, dx", "reference_antiderivative": "-cos(6*x + 12)/3", "category": "trigonometric", "variable": "x"}
{"id": "atom-0366", "stage": "atomic", "k": 1, "integrand": "5*cos(10*x + 4)", "integrand_latex": "5 \\cos{\\left(10 x + 4 \\right)}", "integrand_latex_integral": "\\int 5 \\cos{\\left(10 x + 4 \\right)} \\, dx", "reference_antiderivative": "sin(10*x + 4)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0367", "stage": "atomic", "k": 1, "integrand": "2*sin(4*x + 2)", "integrand_latex": "2 \\sin{\\left(4 x + 2 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(4 x + 2 \\right)} \\, dx", "reference_antiderivative": "-cos(4*x + 2)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0368", "stage": "atomic", "k": 1, "integrand": "-4*sin(8*x - 7)", "integrand_latex": "- 4 \\sin{\\left(8 x - 7 \\right)}", "integrand_latex_integral": "\\int - 4 \\sin{\\left(8 x - 7 \\right)} \\, dx", "reference_antiderivative": "cos(8*x - 7)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0369", "stage": "atomic", "k": 1, "integrand": "-5*sin(4*x - 4)", "integrand_latex": "- 5 \\sin{\\left(4 x - 4 \\right)}", "integrand_latex_integral": "\\int - 5 \\sin{\\left(4 x - 4 \\right)} \\, dx", "reference_antiderivative": "5*cos(4*x - 4)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0370", "stage": "atomic", "k": 1, "integrand": "-3*sin(6*x + 6)", "integrand_latex": "- 3 \\sin{\\left(6 x + 6 \\right)}", "integrand_latex_integral": "\\int - 3 \\sin{\\left(6 x + 6 \\right)} \\, dx", "reference_antiderivative": "cos(6*x + 6)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0371", "stage": "atomic", "k": 1, "integrand": "-4*tan(15*x + 1)", "integrand_latex": "- 4 \\tan{\\left(15 x + 1 \\right)}", "integrand_latex_integral": "\\int - 4 \\tan{\\left(15 x + 1 \\right)} \\, dx", "reference_antiderivative": "-2*log(tan(15*x + 1)**2 + 1)/15", "category": "trigonometric", "variable": "x"}
{"id": "atom-0372", "stage": "atomic", "k": 1, "integrand": "3*cos(2*x - 15)", "integrand_latex": "3 \\cos{\\left(2 x - 15 \\right)}", "integrand_latex_integral": "\\int 3 \\cos{\\left(2 x - 15 \\right)} \\, dx", "reference_antiderivative": "3*sin(2*x - 15)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0373", "stage": "atomic", "k": 1, "integrand": "-5*cos(5*x - 3)", "integrand_latex": "- 5 \\cos{\\left(5 x - 3 \\right)}", "integrand_latex_integral": "\\int - 5 \\cos{\\left(5 x - 3 \\right)} \\, dx", "reference_antiderivative": "-sin(5*x - 3)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0374", "stage": "atomic", "k": 1, "integrand": "5*sin(4*x - 10)", "integrand_latex": "5 \\sin{\\left(4 x - 10 \\right)}", "integrand_latex_integral": "\\int 5 \\sin{\\left(4 x - 10 \\right)} \\, dx", "reference_antiderivative": "-5*cos(4*x - 10)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0375", "stage": "atomic", "k": 1, "integrand": "5*tan(5*x - 12)", "integrand_latex": "5 \\tan{\\left(5 x - 12 \\right)}", "integrand_latex_integral": "\\int 5 \\tan{\\left(5 x - 12 \\right)} \\, dx", "reference_antiderivative": "log(tan(5*x - 12)**2 + 1)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0376", "stage": "atomic", "k": 1, "integrand": "3*tan(14*x + 4)", "integrand_latex": "3 \\tan{\\left(14 x + 4 \\right)}", "integrand_latex_integral": "\\int 3 \\tan{\\left(14 x + 4 \\right)} \\, dx", "reference_antiderivative": "3*log(tan(14*x + 4)**2 + 1)/28", "category": "trigonometric", "variable": "x"}
{"id": "atom-0377", "stage": "atomic", "k": 1, "integrand": "-5*tan(10*x - 11)", "integrand_latex": "- 5 \\tan{\\left(10 x - 11 \\right)}", "integrand_latex_integral": "\\int - 5 \\tan{\\left(10 x - 11 \\right)} \\, dx", "reference_antiderivative": "-log(tan(10*x - 11)**2 + 1)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0378", "stage": "atomic", "k": 1, "integrand": "2*sin(5*x - 10)", "integrand_latex": "2 \\sin{\\left(5 x - 10 \\right)}", "integrand_latex_integral": "\\int 2 \\sin{\\left(5 x - 10 \\right)} \\, dx", "reference_antiderivative": "-2*cos(5*x - 10)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0379", "stage": "atomic", "k": 1, "integrand": "-2*sin(14*x + 6)", "integrand_latex": "- 2 \\sin{\\left(14 x + 6 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(14 x + 6 \\right)} \\, dx", "reference_antiderivative": "cos(14*x + 6)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0380", "stage": "atomic", "k": 1, "integrand": "-2*cos(13*x - 14)", "integrand_latex": "- 2 \\cos{\\left(13 x - 14 \\right)}", "integrand_latex_integral": "\\int - 2 \\cos{\\left(13 x - 14 \\right)} \\, dx", "reference_antiderivative": "-2*sin(13*x - 14)/13", "category": "trigonometric", "variable": "x"}
{"id": "atom-0381", "stage": "atomic", "k": 1, "integrand": "-3*tan(3*x - 11)", "integrand_latex": "- 3 \\tan{\\left(3 x - 11 \\right)}", "integrand_latex_integral": "\\int - 3 \\tan{\\left(3 x - 11 \\right)} \\, dx", "reference_antiderivative": "-log(tan(3*x - 11)**2 + 1)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0382", "stage": "atomic", "k": 1, "integrand": "-5*sin(9*x + 5)", "integrand_latex": "- 5 \\sin{\\left(9 x + 5 \\right)}", "integrand_latex_integral": "\\int - 5 \\sin{\\left(9 x + 5 \\right)} \\, dx", "reference_antiderivative": "5*cos(9*x + 5)/9", "category": "trigonometric", "variable": "x"}
{"id": "atom-0383", "stage": "atomic", "k": 1, "integrand": "-5*cos(12*x + 5)", "integrand_latex": "- 5 \\cos{\\left(12 x + 5 \\right)}", "integrand_latex_integral": "\\int - 5 \\cos{\\left(12 x + 5 \\right)} \\, dx", "reference_antiderivative": "-5*sin(12*x + 5)/12", "category": "trigonometric", "variable": "x"}
{"id": "atom-0384", "stage": "atomic", "k": 1, "integrand": "tan(13*x - 3)", "integrand_latex": "\\tan{\\left(13 x - 3 \\right)}", "integrand_latex_integral": "\\int \\tan{\\left(13 x - 3 \\right)} \\, dx", "reference_antiderivative": "log(tan(13*x - 3)**2 + 1)/26", "category": "trigonometric", "variable": "x"}
{"id": "atom-0385", "stage": "atomic", "k": 1, "integrand": "4*sin(2*x - 4)", "integrand_latex": "4 \\sin{\\left(2 x - 4 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(2 x - 4 \\right)} \\, dx", "reference_antiderivative": "-2*cos(2*x - 4)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0386", "stage": "atomic", "k": 1, "integrand": "4*tan(13*x + 5)", "integrand_latex": "4 \\tan{\\left(13 x + 5 \\right)}", "integrand_latex_integral": "\\int 4 \\tan{\\left(13 x + 5 \\right)} \\, dx", "reference_antiderivative": "2*log(tan(13*x + 5)**2 + 1)/13", "category": "trigonometric", "variable": "x"}
{"id": "atom-0387", "stage": "atomic", "k": 1, "integrand": "2*cos(4*x + 7)", "integrand_latex": "2 \\cos{\\left(4 x + 7 \\right)}", "integrand_latex_integral": "\\int 2 \\cos{\\left(4 x + 7 \\right)} \\, dx", "reference_antiderivative": "sin(4*x + 7)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0388", "stage": "atomic", "k": 1, "integrand": "-2*sin(4*x + 1)", "integrand_latex": "- 2 \\sin{\\left(4 x + 1 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(4 x + 1 \\right)} \\, dx", "reference_antiderivative": "cos(4*x + 1)/2", "category": "trigonometric", "variable": "x"}
{"id": "atom-0389", "stage": "atomic", "k": 1, "integrand": "-4*tan(2*x + 7)", "integrand_latex": "- 4 \\tan{\\left(2 x + 7 \\right)}", "integrand_latex_integral": "\\int - 4 \\tan{\\left(2 x + 7 \\right)} \\, dx", "reference_antiderivative": "-log(tan(2*x + 7)**2 + 1)", "category": "trigonometric", "variable": "x"}
{"id": "atom-0390", "stage": "atomic", "k": 1, "integrand": "5*tan(13*x - 6)", "integrand_latex": "5 \\tan{\\left(13 x - 6 \\right)}", "integrand_latex_integral": "\\int 5 \\tan{\\left(13 x - 6 \\right)} \\, dx", "reference_antiderivative": "5*log(tan(13*x - 6)**2 + 1)/26", "category": "trigonometric", "variable": "x"}
{"id": "atom-0391", "stage": "atomic", "k": 1, "integrand": "3*tan(10*x + 8)", "integrand_latex": "3 \\tan{\\left(10 x + 8 \\right)}", "integrand_latex_integral": "\\int 3 \\tan{\\left(10 x + 8 \\right)} \\, dx", "reference_antiderivative": "3*log(tan(10*x + 8)**2 + 1)/20", "category": "trigonometric", "variable": "x"}
{"id": "atom-0392", "stage": "atomic", "k": 1, "integrand": "5*tan(11*x - 12)", "integrand_latex": "5 \\tan{\\left(11 x - 12 \\right)}", "integrand_latex_integral": "\\int 5 \\tan{\\left(11 x - 12 \\right)} \\, dx", "reference_antiderivative": "5*log(tan(11*x - 12)**2 + 1)/22", "category": "trigonometric", "variable": "x"}
{"id": "atom-0393", "stage": "atomic", "k": 1, "integrand": "-2*sin(14*x + 11)", "integrand_latex": "- 2 \\sin{\\left(14 x + 11 \\right)}", "integrand_latex_integral": "\\int - 2 \\sin{\\left(14 x + 11 \\right)} \\, dx", "reference_antiderivative": "cos(14*x + 11)/7", "category": "trigonometric", "variable": "x"}
{"id": "atom-0394", "stage": "atomic", "k": 1, "integrand": "5*cos(4*x + 4)", "integrand_latex": "5 \\cos{\\left(4 x + 4 \\right)}", "integrand_latex_integral": "\\int 5 \\cos{\\left(4 x + 4 \\right)} \\, dx", "reference_antiderivative": "5*sin(4*x + 4)/4", "category": "trigonometric", "variable": "x"}
{"id": "atom-0395", "stage": "atomic", "k": 1, "integrand": "-5*tan(4*x - 11)", "integrand_latex": "- 5 \\tan{\\left(4 x - 11 \\right)}", "integrand_latex_integral": "\\int - 5 \\tan{\\left(4 x - 11 \\right)} \\, dx", "reference_antiderivative": "-5*log(tan(4*x - 11)**2 + 1)/8", "category": "trigonometric", "variable": "x"}
{"id": "atom-0396", "stage": "atomic", "k": 1, "integrand": "2*tan(9*x - 13)", "integrand_latex": "2 \\tan{\\left(9 x - 13 \\right)}", "integrand_latex_integral": "\\int 2 \\tan{\\left(9 x - 13 \\right)} \\, dx", "reference_antiderivative": "log(tan(9*x - 13)**2 + 1)/9", "category": "trigonometric", "variable": "x"}
{"id": "atom-0397", "stage": "atomic", "k": 1, "integrand": "cos(5*x - 5)", "integrand_latex": "\\cos{\\left(5 x - 5 \\right)}", "integrand_latex_integral": "\\int \\cos{\\left(5 x - 5 \\right)} \\, dx", "reference_antiderivative": "sin(5*x - 5)/5", "category": "trigonometric", "variable": "x"}
{"id": "atom-0398", "stage": "atomic", "k": 1, "integrand": "4*sin(15*x - 8)", "integrand_latex": "4 \\sin{\\left(15 x - 8 \\right)}", "integrand_latex_integral": "\\int 4 \\sin{\\left(15 x - 8 \\right)} \\, dx", "reference_antiderivative": "-4*cos(15*x - 8)/15", "category": "trigonometric", "variable": "x"}
{"id": "atom-0399", "stage": "atomic", "k": 1, "integrand": "sin(14*x + 2)", "integrand_latex": "\\sin{\\left(14 x + 2 \\right)}", "integrand_latex_integral": "\\int \\sin{\\left(14 x + 2 \\right)} \\, dx", "reference_antiderivative": "-cos(14*x + 2)/14", "category": "trigonometric", "variable": "x"}
{"id": "atom-0400", "stage": "atomic", "k": 1, "integrand": "-exp(7*x)", "integrand_latex": "- e^{7 x}", "integrand_latex_integral": "\\int - e^{7 x} \\, dx", "reference_antiderivative": "-exp(7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0401", "stage": "atomic", "k": 1, "integrand": "4*exp(-6*x)", "integrand_latex": "4 e^{- 6 x}", "integrand_latex_integral": "\\int 4 e^{- 6 x} \\, dx", "reference_antiderivative": "-2*exp(-6*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0402", "stage": "atomic", "k": 1, "integrand": "2*exp(-9*x)", "integrand_latex": "2 e^{- 9 x}", "integrand_latex_integral": "\\int 2 e^{- 9 x} \\, dx", "reference_antiderivative": "-2*exp(-9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0403", "stage": "atomic", "k": 1, "integrand": "-4*exp(-x)", "integrand_latex": "- 4 e^{- x}", "integrand_latex_integral": "\\int - 4 e^{- x} \\, dx", "reference_antiderivative": "4*exp(-x)", "category": "exponential", "variable": "x"}
{"id": "atom-0404", "stage": "atomic", "k": 1, "integrand": "2*exp(-13*x)", "integrand_latex": "2 e^{- 13 x}", "integrand_latex_integral": "\\int 2 e^{- 13 x} \\, dx", "reference_antiderivative": "-2*exp(-13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0405", "stage": "atomic", "k": 1, "integrand": "5*exp(-4*x)", "integrand_latex": "5 e^{- 4 x}", "integrand_latex_integral": "\\int 5 e^{- 4 x} \\, dx", "reference_antiderivative": "-5*exp(-4*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0406", "stage": "atomic", "k": 1, "integrand": "3*exp(2*x)", "integrand_latex": "3 e^{2 x}", "integrand_latex_integral": "\\int 3 e^{2 x} \\, dx", "reference_antiderivative": "3*exp(2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0407", "stage": "atomic", "k": 1, "integrand": "-exp(12*x)", "integrand_latex": "- e^{12 x}", "integrand_latex_integral": "\\int - e^{12 x} \\, dx", "reference_antiderivative": "-exp(12*x)/12", "category": "exponential", "variable": "x"}
{"id": "atom-0408", "stage": "atomic", "k": 1, "integrand": "5*exp(-10*x)", "integrand_latex": "5 e^{- 10 x}", "integrand_latex_integral": "\\int 5 e^{- 10 x} \\, dx", "reference_antiderivative": "-exp(-10*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0409", "stage": "atomic", "k": 1, "integrand": "3*exp(-8*x)", "integrand_latex": "3 e^{- 8 x}", "integrand_latex_integral": "\\int 3 e^{- 8 x} \\, dx", "reference_antiderivative": "-3*exp(-8*x)/8", "category": "exponential", "variable": "x"}
{"id": "atom-0410", "stage": "atomic", "k": 1, "integrand": "-2*exp(10*x)", "integrand_latex": "- 2 e^{10 x}", "integrand_latex_integral": "\\int - 2 e^{10 x} \\, dx", "reference_antiderivative": "-exp(10*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0411", "stage": "atomic", "k": 1, "integrand": "2*exp(-15*x)", "integrand_latex": "2 e^{- 15 x}", "integrand_latex_integral": "\\int 2 e^{- 15 x} \\, dx", "reference_antiderivative": "-2*exp(-15*x)/15", "category": "exponential", "variable": "x"}
{"id": "atom-0412", "stage": "atomic", "k": 1, "integrand": "4*exp(-4*x)", "integrand_latex": "4 e^{- 4 x}", "integrand_latex_integral": "\\int 4 e^{- 4 x} \\, dx", "reference_antiderivative": "-exp(-4*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0413", "stage": "atomic", "k": 1, "integrand": "3*exp(-11*x)", "integrand_latex": "3 e^{- 11 x}", "integrand_latex_integral": "\\int 3 e^{- 11 x} \\, dx", "reference_antiderivative": "-3*exp(-11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0414", "stage": "atomic", "k": 1, "integrand": "-4*exp(-13*x)", "integrand_latex": "- 4 e^{- 13 x}", "integrand_latex_integral": "\\int - 4 e^{- 13 x} \\, dx", "reference_antiderivative": "4*exp(-13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0415", "stage": "atomic", "k": 1, "integrand": "2*exp(x)", "integrand_latex": "2 e^{x}", "integrand_latex_integral": "\\int 2 e^{x} \\, dx", "reference_antiderivative": "2*exp(x)", "category": "exponential", "variable": "x"}
{"id": "atom-0416", "stage": "atomic", "k": 1, "integrand": "exp(11*x)", "integrand_latex": "e^{11 x}", "integrand_latex_integral": "\\int e^{11 x} \\, dx", "reference_antiderivative": "exp(11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0417", "stage": "atomic", "k": 1, "integrand": "-3*exp(-5*x)", "integrand_latex": "- 3 e^{- 5 x}", "integrand_latex_integral": "\\int - 3 e^{- 5 x} \\, dx", "reference_antiderivative": "3*exp(-5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0418", "stage": "atomic", "k": 1, "integrand": "2*exp(-x)", "integrand_latex": "2 e^{- x}", "integrand_latex_integral": "\\int 2 e^{- x} \\, dx", "reference_antiderivative": "-2*exp(-x)", "category": "exponential", "variable": "x"}
{"id": "atom-0419", "stage": "atomic", "k": 1, "integrand": "-3*exp(13*x)", "integrand_latex": "- 3 e^{13 x}", "integrand_latex_integral": "\\int - 3 e^{13 x} \\, dx", "reference_antiderivative": "-3*exp(13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0420", "stage": "atomic", "k": 1, "integrand": "3*exp(5*x)", "integrand_latex": "3 e^{5 x}", "integrand_latex_integral": "\\int 3 e^{5 x} \\, dx", "reference_antiderivative": "3*exp(5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0421", "stage": "atomic", "k": 1, "integrand": "-3*exp(-2*x)", "integrand_latex": "- 3 e^{- 2 x}", "integrand_latex_integral": "\\int - 3 e^{- 2 x} \\, dx", "reference_antiderivative": "3*exp(-2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0422", "stage": "atomic", "k": 1, "integrand": "-5*exp(11*x)", "integrand_latex": "- 5 e^{11 x}", "integrand_latex_integral": "\\int - 5 e^{11 x} \\, dx", "reference_antiderivative": "-5*exp(11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0423", "stage": "atomic", "k": 1, "integrand": "-3*exp(-6*x)", "integrand_latex": "- 3 e^{- 6 x}", "integrand_latex_integral": "\\int - 3 e^{- 6 x} \\, dx", "reference_antiderivative": "exp(-6*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0424", "stage": "atomic", "k": 1, "integrand": "-2*exp(-4*x)", "integrand_latex": "- 2 e^{- 4 x}", "integrand_latex_integral": "\\int - 2 e^{- 4 x} \\, dx", "reference_antiderivative": "exp(-4*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0425", "stage": "atomic", "k": 1, "integrand": "3*exp(13*x)", "integrand_latex": "3 e^{13 x}", "integrand_latex_integral": "\\int 3 e^{13 x} \\, dx", "reference_antiderivative": "3*exp(13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0426", "stage": "atomic", "k": 1, "integrand": "-4*exp(-7*x)", "integrand_latex": "- 4 e^{- 7 x}", "integrand_latex_integral": "\\int - 4 e^{- 7 x} \\, dx", "reference_antiderivative": "4*exp(-7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0427", "stage": "atomic", "k": 1, "integrand": "3*exp(-7*x)", "integrand_latex": "3 e^{- 7 x}", "integrand_latex_integral": "\\int 3 e^{- 7 x} \\, dx", "reference_antiderivative": "-3*exp(-7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0428", "stage": "atomic", "k": 1, "integrand": "-exp(4*x)", "integrand_latex": "- e^{4 x}", "integrand_latex_integral": "\\int - e^{4 x} \\, dx", "reference_antiderivative": "-exp(4*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0429", "stage": "atomic", "k": 1, "integrand": "4*exp(-11*x)", "integrand_latex": "4 e^{- 11 x}", "integrand_latex_integral": "\\int 4 e^{- 11 x} \\, dx", "reference_antiderivative": "-4*exp(-11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0430", "stage": "atomic", "k": 1, "integrand": "4*exp(8*x)", "integrand_latex": "4 e^{8 x}", "integrand_latex_integral": "\\int 4 e^{8 x} \\, dx", "reference_antiderivative": "exp(8*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0431", "stage": "atomic", "k": 1, "integrand": "4*exp(-14*x)", "integrand_latex": "4 e^{- 14 x}", "integrand_latex_integral": "\\int 4 e^{- 14 x} \\, dx", "reference_antiderivative": "-2*exp(-14*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0432", "stage": "atomic", "k": 1, "integrand": "-5*exp(-13*x)", "integrand_latex": "- 5 e^{- 13 x}", "integrand_latex_integral": "\\int - 5 e^{- 13 x} \\, dx", "reference_antiderivative": "5*exp(-13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0433", "stage": "atomic", "k": 1, "integrand": "5*exp(9*x)", "integrand_latex": "5 e^{9 x}", "integrand_latex_integral": "\\int 5 e^{9 x} \\, dx", "reference_antiderivative": "5*exp(9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0434", "stage": "atomic", "k": 1, "integrand": "5*exp(-9*x)", "integrand_latex": "5 e^{- 9 x}", "integrand_latex_integral": "\\int 5 e^{- 9 x} \\, dx", "reference_antiderivative": "-5*exp(-9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0435", "stage": "atomic", "k": 1, "integrand": "exp(4*x)", "integrand_latex": "e^{4 x}", "integrand_latex_integral": "\\int e^{4 x} \\, dx", "reference_antiderivative": "exp(4*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0436", "stage": "atomic", "k": 1, "integrand": "2*exp(13*x)", "integrand_latex": "2 e^{13 x}", "integrand_latex_integral": "\\int 2 e^{13 x} \\, dx", "reference_antiderivative": "2*exp(13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0437", "stage": "atomic", "k": 1, "integrand": "-exp(5*x)", "integrand_latex": "- e^{5 x}", "integrand_latex_integral": "\\int - e^{5 x} \\, dx", "reference_antiderivative": "-exp(5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0438", "stage": "atomic", "k": 1, "integrand": "2*exp(-8*x)", "integrand_latex": "2 e^{- 8 x}", "integrand_latex_integral": "\\int 2 e^{- 8 x} \\, dx", "reference_antiderivative": "-exp(-8*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0439", "stage": "atomic", "k": 1, "integrand": "5*exp(-3*x)", "integrand_latex": "5 e^{- 3 x}", "integrand_latex_integral": "\\int 5 e^{- 3 x} \\, dx", "reference_antiderivative": "-5*exp(-3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0440", "stage": "atomic", "k": 1, "integrand": "-4*exp(7*x)", "integrand_latex": "- 4 e^{7 x}", "integrand_latex_integral": "\\int - 4 e^{7 x} \\, dx", "reference_antiderivative": "-4*exp(7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0441", "stage": "atomic", "k": 1, "integrand": "2*exp(-2*x)", "integrand_latex": "2 e^{- 2 x}", "integrand_latex_integral": "\\int 2 e^{- 2 x} \\, dx", "reference_antiderivative": "-exp(-2*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0442", "stage": "atomic", "k": 1, "integrand": "-2*exp(-5*x)", "integrand_latex": "- 2 e^{- 5 x}", "integrand_latex_integral": "\\int - 2 e^{- 5 x} \\, dx", "reference_antiderivative": "2*exp(-5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0443", "stage": "atomic", "k": 1, "integrand": "exp(-11*x)", "integrand_latex": "e^{- 11 x}", "integrand_latex_integral": "\\int e^{- 11 x} \\, dx", "reference_antiderivative": "-exp(-11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0444", "stage": "atomic", "k": 1, "integrand": "-2*exp(-x)", "integrand_latex": "- 2 e^{- x}", "integrand_latex_integral": "\\int - 2 e^{- x} \\, dx", "reference_antiderivative": "2*exp(-x)", "category": "exponential", "variable": "x"}
{"id": "atom-0445", "stage": "atomic", "k": 1, "integrand": "-5*exp(-6*x)", "integrand_latex": "- 5 e^{- 6 x}", "integrand_latex_integral": "\\int - 5 e^{- 6 x} \\, dx", "reference_antiderivative": "5*exp(-6*x)/6", "category": "exponential", "variable": "x"}
{"id": "atom-0446", "stage": "atomic", "k": 1, "integrand": "4*exp(-2*x)", "integrand_latex": "4 e^{- 2 x}", "integrand_latex_integral": "\\int 4 e^{- 2 x} \\, dx", "reference_antiderivative": "-2*exp(-2*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0447", "stage": "atomic", "k": 1, "integrand": "-3*exp(11*x)", "integrand_latex": "- 3 e^{11 x}", "integrand_latex_integral": "\\int - 3 e^{11 x} \\, dx", "reference_antiderivative": "-3*exp(11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0448", "stage": "atomic", "k": 1, "integrand": "-3*exp(x)", "integrand_latex": "- 3 e^{x}", "integrand_latex_integral": "\\int - 3 e^{x} \\, dx", "reference_antiderivative": "-3*exp(x)", "category": "exponential", "variable": "x"}
{"id": "atom-0449", "stage": "atomic", "k": 1, "integrand": "-exp(-15*x)", "integrand_latex": "- e^{- 15 x}", "integrand_latex_integral": "\\int - e^{- 15 x} \\, dx", "reference_antiderivative": "exp(-15*x)/15", "category": "exponential", "variable": "x"}
{"id": "atom-0450", "stage": "atomic", "k": 1, "integrand": "exp(x)", "integrand_latex": "e^{x}", "integrand_latex_integral": "\\int e^{x} \\, dx", "reference_antiderivative": "exp(x)", "category": "exponential", "variable": "x"}
{"id": "atom-0451", "stage": "atomic", "k": 1, "integrand": "-2*exp(-9*x)", "integrand_latex": "- 2 e^{- 9 x}", "integrand_latex_integral": "\\int - 2 e^{- 9 x} \\, dx", "reference_antiderivative": "2*exp(-9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0452", "stage": "atomic", "k": 1, "integrand": "-5*exp(-14*x)", "integrand_latex": "- 5 e^{- 14 x}", "integrand_latex_integral": "\\int - 5 e^{- 14 x} \\, dx", "reference_antiderivative": "5*exp(-14*x)/14", "category": "exponential", "variable": "x"}
{"id": "atom-0453", "stage": "atomic", "k": 1, "integrand": "4*exp(13*x)", "integrand_latex": "4 e^{13 x}", "integrand_latex_integral": "\\int 4 e^{13 x} \\, dx", "reference_antiderivative": "4*exp(13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0454", "stage": "atomic", "k": 1, "integrand": "5*exp(-6*x)", "integrand_latex": "5 e^{- 6 x}", "integrand_latex_integral": "\\int 5 e^{- 6 x} \\, dx", "reference_antiderivative": "-5*exp(-6*x)/6", "category": "exponential", "variable": "x"}
{"id": "atom-0455", "stage": "atomic", "k": 1, "integrand": "-4*exp(-2*x)", "integrand_latex": "- 4 e^{- 2 x}", "integrand_latex_integral": "\\int - 4 e^{- 2 x} \\, dx", "reference_antiderivative": "2*exp(-2*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0456", "stage": "atomic", "k": 1, "integrand": "-exp(8*x)", "integrand_latex": "- e^{8 x}", "integrand_latex_integral": "\\int - e^{8 x} \\, dx", "reference_antiderivative": "-exp(8*x)/8", "category": "exponential", "variable": "x"}
{"id": "atom-0457", "stage": "atomic", "k": 1, "integrand": "exp(-4*x)", "integrand_latex": "e^{- 4 x}", "integrand_latex_integral": "\\int e^{- 4 x} \\, dx", "reference_antiderivative": "-exp(-4*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0458", "stage": "atomic", "k": 1, "integrand": "-5*exp(3*x)", "integrand_latex": "- 5 e^{3 x}", "integrand_latex_integral": "\\int - 5 e^{3 x} \\, dx", "reference_antiderivative": "-5*exp(3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0459", "stage": "atomic", "k": 1, "integrand": "3*exp(-6*x)", "integrand_latex": "3 e^{- 6 x}", "integrand_latex_integral": "\\int 3 e^{- 6 x} \\, dx", "reference_antiderivative": "-exp(-6*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0460", "stage": "atomic", "k": 1, "integrand": "3*exp(-x)", "integrand_latex": "3 e^{- x}", "integrand_latex_integral": "\\int 3 e^{- x} \\, dx", "reference_antiderivative": "-3*exp(-x)", "category": "exponential", "variable": "x"}
{"id": "atom-0461", "stage": "atomic", "k": 1, "integrand": "-exp(11*x)", "integrand_latex": "- e^{11 x}", "integrand_latex_integral": "\\int - e^{11 x} \\, dx", "reference_antiderivative": "-exp(11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0462", "stage": "atomic", "k": 1, "integrand": "5*exp(4*x)", "integrand_latex": "5 e^{4 x}", "integrand_latex_integral": "\\int 5 e^{4 x} \\, dx", "reference_antiderivative": "5*exp(4*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0463", "stage": "atomic", "k": 1, "integrand": "-4*exp(-3*x)", "integrand_latex": "- 4 e^{- 3 x}", "integrand_latex_integral": "\\int - 4 e^{- 3 x} \\, dx", "reference_antiderivative": "4*exp(-3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0464", "stage": "atomic", "k": 1, "integrand": "3*exp(15*x)", "integrand_latex": "3 e^{15 x}", "integrand_latex_integral": "\\int 3 e^{15 x} \\, dx", "reference_antiderivative": "exp(15*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0465", "stage": "atomic", "k": 1, "integrand": "-3*exp(-9*x)", "integrand_latex": "- 3 e^{- 9 x}", "integrand_latex_integral": "\\int - 3 e^{- 9 x} \\, dx", "reference_antiderivative": "exp(-9*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0466", "stage": "atomic", "k": 1, "integrand": "-5*exp(-11*x)", "integrand_latex": "- 5 e^{- 11 x}", "integrand_latex_integral": "\\int - 5 e^{- 11 x} \\, dx", "reference_antiderivative": "5*exp(-11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0467", "stage": "atomic", "k": 1, "integrand": "4*exp(-5*x)", "integrand_latex": "4 e^{- 5 x}", "integrand_latex_integral": "\\int 4 e^{- 5 x} \\, dx", "reference_antiderivative": "-4*exp(-5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0468", "stage": "atomic", "k": 1, "integrand": "-5*exp(-4*x)", "integrand_latex": "- 5 e^{- 4 x}", "integrand_latex_integral": "\\int - 5 e^{- 4 x} \\, dx", "reference_antiderivative": "5*exp(-4*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0469", "stage": "atomic", "k": 1, "integrand": "5*exp(-15*x)", "integrand_latex": "5 e^{- 15 x}", "integrand_latex_integral": "\\int 5 e^{- 15 x} \\, dx", "reference_antiderivative": "-exp(-15*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0470", "stage": "atomic", "k": 1, "integrand": "-exp(15*x)", "integrand_latex": "- e^{15 x}", "integrand_latex_integral": "\\int - e^{15 x} \\, dx", "reference_antiderivative": "-exp(15*x)/15", "category": "exponential", "variable": "x"}
{"id": "atom-0471", "stage": "atomic", "k": 1, "integrand": "4*exp(3*x)", "integrand_latex": "4 e^{3 x}", "integrand_latex_integral": "\\int 4 e^{3 x} \\, dx", "reference_antiderivative": "4*exp(3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0472", "stage": "atomic", "k": 1, "integrand": "-2*exp(-14*x)", "integrand_latex": "- 2 e^{- 14 x}", "integrand_latex_integral": "\\int - 2 e^{- 14 x} \\, dx", "reference_antiderivative": "exp(-14*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0473", "stage": "atomic", "k": 1, "integrand": "-4*exp(-9*x)", "integrand_latex": "- 4 e^{- 9 x}", "integrand_latex_integral": "\\int - 4 e^{- 9 x} \\, dx", "reference_antiderivative": "4*exp(-9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0474", "stage": "atomic", "k": 1, "integrand": "-2*exp(-2*x)", "integrand_latex": "- 2 e^{- 2 x}", "integrand_latex_integral": "\\int - 2 e^{- 2 x} \\, dx", "reference_antiderivative": "exp(-2*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0475", "stage": "atomic", "k": 1, "integrand": "4*exp(14*x)", "integrand_latex": "4 e^{14 x}", "integrand_latex_integral": "\\int 4 e^{14 x} \\, dx", "reference_antiderivative": "2*exp(14*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0476", "stage": "atomic", "k": 1, "integrand": "-5*exp(7*x)", "integrand_latex": "- 5 e^{7 x}", "integrand_latex_integral": "\\int - 5 e^{7 x} \\, dx", "reference_antiderivative": "-5*exp(7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0477", "stage": "atomic", "k": 1, "integrand": "-2*exp(2*x)", "integrand_latex": "- 2 e^{2 x}", "integrand_latex_integral": "\\int - 2 e^{2 x} \\, dx", "reference_antiderivative": "-exp(2*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0478", "stage": "atomic", "k": 1, "integrand": "5*exp(x)", "integrand_latex": "5 e^{x}", "integrand_latex_integral": "\\int 5 e^{x} \\, dx", "reference_antiderivative": "5*exp(x)", "category": "exponential", "variable": "x"}
{"id": "atom-0479", "stage": "atomic", "k": 1, "integrand": "-3*exp(-x)", "integrand_latex": "- 3 e^{- x}", "integrand_latex_integral": "\\int - 3 e^{- x} \\, dx", "reference_antiderivative": "3*exp(-x)", "category": "exponential", "variable": "x"}
{"id": "atom-0480", "stage": "atomic", "k": 1, "integrand": "3*exp(-4*x)", "integrand_latex": "3 e^{- 4 x}", "integrand_latex_integral": "\\int 3 e^{- 4 x} \\, dx", "reference_antiderivative": "-3*exp(-4*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0481", "stage": "atomic", "k": 1, "integrand": "5*exp(5*x)", "integrand_latex": "5 e^{5 x}", "integrand_latex_integral": "\\int 5 e^{5 x} \\, dx", "reference_antiderivative": "exp(5*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0482", "stage": "atomic", "k": 1, "integrand": "-2*exp(-7*x)", "integrand_latex": "- 2 e^{- 7 x}", "integrand_latex_integral": "\\int - 2 e^{- 7 x} \\, dx", "reference_antiderivative": "2*exp(-7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0483", "stage": "atomic", "k": 1, "integrand": "-2*exp(15*x)", "integrand_latex": "- 2 e^{15 x}", "integrand_latex_integral": "\\int - 2 e^{15 x} \\, dx", "reference_antiderivative": "-2*exp(15*x)/15", "category": "exponential", "variable": "x"}
{"id": "atom-0484", "stage": "atomic", "k": 1, "integrand": "-exp(9*x)", "integrand_latex": "- e^{9 x}", "integrand_latex_integral": "\\int - e^{9 x} \\, dx", "reference_antiderivative": "-exp(9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0485", "stage": "atomic", "k": 1, "integrand": "-2*exp(7*x)", "integrand_latex": "- 2 e^{7 x}", "integrand_latex_integral": "\\int - 2 e^{7 x} \\, dx", "reference_antiderivative": "-2*exp(7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0486", "stage": "atomic", "k": 1, "integrand": "2*exp(-4*x)", "integrand_latex": "2 e^{- 4 x}", "integrand_latex_integral": "\\int 2 e^{- 4 x} \\, dx", "reference_antiderivative": "-exp(-4*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0487", "stage": "atomic", "k": 1, "integrand": "-exp(-6*x)", "integrand_latex": "- e^{- 6 x}", "integrand_latex_integral": "\\int - e^{- 6 x} \\, dx", "reference_antiderivative": "exp(-6*x)/6", "category": "exponential", "variable": "x"}
{"id": "atom-0488", "stage": "atomic", "k": 1, "integrand": "5*exp(2*x)", "integrand_latex": "5 e^{2 x}", "integrand_latex_integral": "\\int 5 e^{2 x} \\, dx", "reference_antiderivative": "5*exp(2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0489", "stage": "atomic", "k": 1, "integrand": "-4*exp(-4*x)", "integrand_latex": "- 4 e^{- 4 x}", "integrand_latex_integral": "\\int - 4 e^{- 4 x} \\, dx", "reference_antiderivative": "exp(-4*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0490", "stage": "atomic", "k": 1, "integrand": "5*exp(-7*x)", "integrand_latex": "5 e^{- 7 x}", "integrand_latex_integral": "\\int 5 e^{- 7 x} \\, dx", "reference_antiderivative": "-5*exp(-7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0491", "stage": "atomic", "k": 1, "integrand": "-exp(14*x)", "integrand_latex": "- e^{14 x}", "integrand_latex_integral": "\\int - e^{14 x} \\, dx", "reference_antiderivative": "-exp(14*x)/14", "category": "exponential", "variable": "x"}
{"id": "atom-0492", "stage": "atomic", "k": 1, "integrand": "-exp(-11*x)", "integrand_latex": "- e^{- 11 x}", "integrand_latex_integral": "\\int - e^{- 11 x} \\, dx", "reference_antiderivative": "exp(-11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0493", "stage": "atomic", "k": 1, "integrand": "4*exp(-8*x)", "integrand_latex": "4 e^{- 8 x}", "integrand_latex_integral": "\\int 4 e^{- 8 x} \\, dx", "reference_antiderivative": "-exp(-8*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0494", "stage": "atomic", "k": 1, "integrand": "5*exp(13*x)", "integrand_latex": "5 e^{13 x}", "integrand_latex_integral": "\\int 5 e^{13 x} \\, dx", "reference_antiderivative": "5*exp(13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0495", "stage": "atomic", "k": 1, "integrand": "5*exp(-8*x)", "integrand_latex": "5 e^{- 8 x}", "integrand_latex_integral": "\\int 5 e^{- 8 x} \\, dx", "reference_antiderivative": "-5*exp(-8*x)/8", "category": "exponential", "variable": "x"}
{"id": "atom-0496", "stage": "atomic", "k": 1, "integrand": "exp(-5*x)", "integrand_latex": "e^{- 5 x}", "integrand_latex_integral": "\\int e^{- 5 x} \\, dx", "reference_antiderivative": "-exp(-5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0497", "stage": "atomic", "k": 1, "integrand": "-4*exp(6*x)", "integrand_latex": "- 4 e^{6 x}", "integrand_latex_integral": "\\int - 4 e^{6 x} \\, dx", "reference_antiderivative": "-2*exp(6*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0498", "stage": "atomic", "k": 1, "integrand": "-5*exp(15*x)", "integrand_latex": "- 5 e^{15 x}", "integrand_latex_integral": "\\int - 5 e^{15 x} \\, dx", "reference_antiderivative": "-exp(15*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0499", "stage": "atomic", "k": 1, "integrand": "2*exp(5*x)", "integrand_latex": "2 e^{5 x}", "integrand_latex_integral": "\\int 2 e^{5 x} \\, dx", "reference_antiderivative": "2*exp(5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0500", "stage": "atomic", "k": 1, "integrand": "-exp(-5*x)", "integrand_latex": "- e^{- 5 x}", "integrand_latex_integral": "\\int - e^{- 5 x} \\, dx", "reference_antiderivative": "exp(-5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0501", "stage": "atomic", "k": 1, "integrand": "-5*exp(14*x)", "integrand_latex": "- 5 e^{14 x}", "integrand_latex_integral": "\\int - 5 e^{14 x} \\, dx", "reference_antiderivative": "-5*exp(14*x)/14", "category": "exponential", "variable": "x"}
{"id": "atom-0502", "stage": "atomic", "k": 1, "integrand": "5*exp(3*x)", "integrand_latex": "5 e^{3 x}", "integrand_latex_integral": "\\int 5 e^{3 x} \\, dx", "reference_antiderivative": "5*exp(3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0503", "stage": "atomic", "k": 1, "integrand": "exp(13*x)", "integrand_latex": "e^{13 x}", "integrand_latex_integral": "\\int e^{13 x} \\, dx", "reference_antiderivative": "exp(13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0504", "stage": "atomic", "k": 1, "integrand": "2*exp(-10*x)", "integrand_latex": "2 e^{- 10 x}", "integrand_latex_integral": "\\int 2 e^{- 10 x} \\, dx", "reference_antiderivative": "-exp(-10*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0505", "stage": "atomic", "k": 1, "integrand": "-exp(13*x)", "integrand_latex": "- e^{13 x}", "integrand_latex_integral": "\\int - e^{13 x} \\, dx", "reference_antiderivative": "-exp(13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0506", "stage": "atomic", "k": 1, "integrand": "-exp(3*x)", "integrand_latex": "- e^{3 x}", "integrand_latex_integral": "\\int - e^{3 x} \\, dx", "reference_antiderivative": "-exp(3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0507", "stage": "atomic", "k": 1, "integrand": "-exp(-x)", "integrand_latex": "- e^{- x}", "integrand_latex_integral": "\\int - e^{- x} \\, dx", "reference_antiderivative": "exp(-x)", "category": "exponential", "variable": "x"}
{"id": "atom-0508", "stage": "atomic", "k": 1, "integrand": "3*exp(x)", "integrand_latex": "3 e^{x}", "integrand_latex_integral": "\\int 3 e^{x} \\, dx", "reference_antiderivative": "3*exp(x)", "category": "exponential", "variable": "x"}
{"id": "atom-0509", "stage": "atomic", "k": 1, "integrand": "-3*exp(12*x)", "integrand_latex": "- 3 e^{12 x}", "integrand_latex_integral": "\\int - 3 e^{12 x} \\, dx", "reference_antiderivative": "-exp(12*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0510", "stage": "atomic", "k": 1, "integrand": "-exp(-9*x)", "integrand_latex": "- e^{- 9 x}", "integrand_latex_integral": "\\int - e^{- 9 x} \\, dx", "reference_antiderivative": "exp(-9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0511", "stage": "atomic", "k": 1, "integrand": "-3*exp(8*x)", "integrand_latex": "- 3 e^{8 x}", "integrand_latex_integral": "\\int - 3 e^{8 x} \\, dx", "reference_antiderivative": "-3*exp(8*x)/8", "category": "exponential", "variable": "x"}
{"id": "atom-0512", "stage": "atomic", "k": 1, "integrand": "-2*exp(-10*x)", "integrand_latex": "- 2 e^{- 10 x}", "integrand_latex_integral": "\\int - 2 e^{- 10 x} \\, dx", "reference_antiderivative": "exp(-10*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0513", "stage": "atomic", "k": 1, "integrand": "exp(6*x)", "integrand_latex": "e^{6 x}", "integrand_latex_integral": "\\int e^{6 x} \\, dx", "reference_antiderivative": "exp(6*x)/6", "category": "exponential", "variable": "x"}
{"id": "atom-0514", "stage": "atomic", "k": 1, "integrand": "-5*exp(-7*x)", "integrand_latex": "- 5 e^{- 7 x}", "integrand_latex_integral": "\\int - 5 e^{- 7 x} \\, dx", "reference_antiderivative": "5*exp(-7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0515", "stage": "atomic", "k": 1, "integrand": "2*exp(9*x)", "integrand_latex": "2 e^{9 x}", "integrand_latex_integral": "\\int 2 e^{9 x} \\, dx", "reference_antiderivative": "2*exp(9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0516", "stage": "atomic", "k": 1, "integrand": "2*exp(-6*x)", "integrand_latex": "2 e^{- 6 x}", "integrand_latex_integral": "\\int 2 e^{- 6 x} \\, dx", "reference_antiderivative": "-exp(-6*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0517", "stage": "atomic", "k": 1, "integrand": "-exp(-4*x)", "integrand_latex": "- e^{- 4 x}", "integrand_latex_integral": "\\int - e^{- 4 x} \\, dx", "reference_antiderivative": "exp(-4*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0518", "stage": "atomic", "k": 1, "integrand": "3*exp(14*x)", "integrand_latex": "3 e^{14 x}", "integrand_latex_integral": "\\int 3 e^{14 x} \\, dx", "reference_antiderivative": "3*exp(14*x)/14", "category": "exponential", "variable": "x"}
{"id": "atom-0519", "stage": "atomic", "k": 1, "integrand": "3*exp(10*x)", "integrand_latex": "3 e^{10 x}", "integrand_latex_integral": "\\int 3 e^{10 x} \\, dx", "reference_antiderivative": "3*exp(10*x)/10", "category": "exponential", "variable": "x"}
{"id": "atom-0520", "stage": "atomic", "k": 1, "integrand": "-2*exp(9*x)", "integrand_latex": "- 2 e^{9 x}", "integrand_latex_integral": "\\int - 2 e^{9 x} \\, dx", "reference_antiderivative": "-2*exp(9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0521", "stage": "atomic", "k": 1, "integrand": "4*exp(12*x)", "integrand_latex": "4 e^{12 x}", "integrand_latex_integral": "\\int 4 e^{12 x} \\, dx", "reference_antiderivative": "exp(12*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0522", "stage": "atomic", "k": 1, "integrand": "-4*exp(14*x)", "integrand_latex": "- 4 e^{14 x}", "integrand_latex_integral": "\\int - 4 e^{14 x} \\, dx", "reference_antiderivative": "-2*exp(14*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0523", "stage": "atomic", "k": 1, "integrand": "3*exp(-9*x)", "integrand_latex": "3 e^{- 9 x}", "integrand_latex_integral": "\\int 3 e^{- 9 x} \\, dx", "reference_antiderivative": "-exp(-9*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0524", "stage": "atomic", "k": 1, "integrand": "-3*exp(-10*x)", "integrand_latex": "- 3 e^{- 10 x}", "integrand_latex_integral": "\\int - 3 e^{- 10 x} \\, dx", "reference_antiderivative": "3*exp(-10*x)/10", "category": "exponential", "variable": "x"}
{"id": "atom-0525", "stage": "atomic", "k": 1, "integrand": "-4*exp(13*x)", "integrand_latex": "- 4 e^{13 x}", "integrand_latex_integral": "\\int - 4 e^{13 x} \\, dx", "reference_antiderivative": "-4*exp(13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0526", "stage": "atomic", "k": 1, "integrand": "-5*exp(-x)", "integrand_latex": "- 5 e^{- x}", "integrand_latex_integral": "\\int - 5 e^{- x} \\, dx", "reference_antiderivative": "5*exp(-x)", "category": "exponential", "variable": "x"}
{"id": "atom-0527", "stage": "atomic", "k": 1, "integrand": "exp(-x)", "integrand_latex": "e^{- x}", "integrand_latex_integral": "\\int e^{- x} \\, dx", "reference_antiderivative": "-exp(-x)", "category": "exponential", "variable": "x"}
{"id": "atom-0528", "stage": "atomic", "k": 1, "integrand": "-2*exp(3*x)", "integrand_latex": "- 2 e^{3 x}", "integrand_latex_integral": "\\int - 2 e^{3 x} \\, dx", "reference_antiderivative": "-2*exp(3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0529", "stage": "atomic", "k": 1, "integrand": "3*exp(-14*x)", "integrand_latex": "3 e^{- 14 x}", "integrand_latex_integral": "\\int 3 e^{- 14 x} \\, dx", "reference_antiderivative": "-3*exp(-14*x)/14", "category": "exponential", "variable": "x"}
{"id": "atom-0530", "stage": "atomic", "k": 1, "integrand": "-exp(-2*x)", "integrand_latex": "- e^{- 2 x}", "integrand_latex_integral": "\\int - e^{- 2 x} \\, dx", "reference_antiderivative": "exp(-2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0531", "stage": "atomic", "k": 1, "integrand": "-3*exp(9*x)", "integrand_latex": "- 3 e^{9 x}", "integrand_latex_integral": "\\int - 3 e^{9 x} \\, dx", "reference_antiderivative": "-exp(9*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0532", "stage": "atomic", "k": 1, "integrand": "5*exp(15*x)", "integrand_latex": "5 e^{15 x}", "integrand_latex_integral": "\\int 5 e^{15 x} \\, dx", "reference_antiderivative": "exp(15*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0533", "stage": "atomic", "k": 1, "integrand": "exp(-3*x)", "integrand_latex": "e^{- 3 x}", "integrand_latex_integral": "\\int e^{- 3 x} \\, dx", "reference_antiderivative": "-exp(-3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0534", "stage": "atomic", "k": 1, "integrand": "5*exp(12*x)", "integrand_latex": "5 e^{12 x}", "integrand_latex_integral": "\\int 5 e^{12 x} \\, dx", "reference_antiderivative": "5*exp(12*x)/12", "category": "exponential", "variable": "x"}
{"id": "atom-0535", "stage": "atomic", "k": 1, "integrand": "-3*exp(2*x)", "integrand_latex": "- 3 e^{2 x}", "integrand_latex_integral": "\\int - 3 e^{2 x} \\, dx", "reference_antiderivative": "-3*exp(2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0536", "stage": "atomic", "k": 1, "integrand": "-5*exp(9*x)", "integrand_latex": "- 5 e^{9 x}", "integrand_latex_integral": "\\int - 5 e^{9 x} \\, dx", "reference_antiderivative": "-5*exp(9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0537", "stage": "atomic", "k": 1, "integrand": "3*exp(-2*x)", "integrand_latex": "3 e^{- 2 x}", "integrand_latex_integral": "\\int 3 e^{- 2 x} \\, dx", "reference_antiderivative": "-3*exp(-2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0538", "stage": "atomic", "k": 1, "integrand": "-2*exp(-8*x)", "integrand_latex": "- 2 e^{- 8 x}", "integrand_latex_integral": "\\int - 2 e^{- 8 x} \\, dx", "reference_antiderivative": "exp(-8*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0539", "stage": "atomic", "k": 1, "integrand": "-3*exp(-7*x)", "integrand_latex": "- 3 e^{- 7 x}", "integrand_latex_integral": "\\int - 3 e^{- 7 x} \\, dx", "reference_antiderivative": "3*exp(-7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0540", "stage": "atomic", "k": 1, "integrand": "-4*exp(-14*x)", "integrand_latex": "- 4 e^{- 14 x}", "integrand_latex_integral": "\\int - 4 e^{- 14 x} \\, dx", "reference_antiderivative": "2*exp(-14*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0541", "stage": "atomic", "k": 1, "integrand": "-5*exp(-8*x)", "integrand_latex": "- 5 e^{- 8 x}", "integrand_latex_integral": "\\int - 5 e^{- 8 x} \\, dx", "reference_antiderivative": "5*exp(-8*x)/8", "category": "exponential", "variable": "x"}
{"id": "atom-0542", "stage": "atomic", "k": 1, "integrand": "-4*exp(4*x)", "integrand_latex": "- 4 e^{4 x}", "integrand_latex_integral": "\\int - 4 e^{4 x} \\, dx", "reference_antiderivative": "-exp(4*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0543", "stage": "atomic", "k": 1, "integrand": "4*exp(6*x)", "integrand_latex": "4 e^{6 x}", "integrand_latex_integral": "\\int 4 e^{6 x} \\, dx", "reference_antiderivative": "2*exp(6*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0544", "stage": "atomic", "k": 1, "integrand": "-exp(-8*x)", "integrand_latex": "- e^{- 8 x}", "integrand_latex_integral": "\\int - e^{- 8 x} \\, dx", "reference_antiderivative": "exp(-8*x)/8", "category": "exponential", "variable": "x"}
{"id": "atom-0545", "stage": "atomic", "k": 1, "integrand": "5*exp(11*x)", "integrand_latex": "5 e^{11 x}", "integrand_latex_integral": "\\int 5 e^{11 x} \\, dx", "reference_antiderivative": "5*exp(11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0546", "stage": "atomic", "k": 1, "integrand": "-exp(-7*x)", "integrand_latex": "- e^{- 7 x}", "integrand_latex_integral": "\\int - e^{- 7 x} \\, dx", "reference_antiderivative": "exp(-7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0547", "stage": "atomic", "k": 1, "integrand": "-3*exp(5*x)", "integrand_latex": "- 3 e^{5 x}", "integrand_latex_integral": "\\int - 3 e^{5 x} \\, dx", "reference_antiderivative": "-3*exp(5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0548", "stage": "atomic", "k": 1, "integrand": "5*exp(6*x)", "integrand_latex": "5 e^{6 x}", "integrand_latex_integral": "\\int 5 e^{6 x} \\, dx", "reference_antiderivative": "5*exp(6*x)/6", "category": "exponential", "variable": "x"}
{"id": "atom-0549", "stage": "atomic", "k": 1, "integrand": "3*exp(-5*x)", "integrand_latex": "3 e^{- 5 x}", "integrand_latex_integral": "\\int 3 e^{- 5 x} \\, dx", "reference_antiderivative": "-3*exp(-5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0550", "stage": "atomic", "k": 1, "integrand": "-2*exp(12*x)", "integrand_latex": "- 2 e^{12 x}", "integrand_latex_integral": "\\int - 2 e^{12 x} \\, dx", "reference_antiderivative": "-exp(12*x)/6", "category": "exponential", "variable": "x"}
{"id": "atom-0551", "stage": "atomic", "k": 1, "integrand": "-3*exp(10*x)", "integrand_latex": "- 3 e^{10 x}", "integrand_latex_integral": "\\int - 3 e^{10 x} \\, dx", "reference_antiderivative": "-3*exp(10*x)/10", "category": "exponential", "variable": "x"}
{"id": "atom-0552", "stage": "atomic", "k": 1, "integrand": "-5*exp(2*x)", "integrand_latex": "- 5 e^{2 x}", "integrand_latex_integral": "\\int - 5 e^{2 x} \\, dx", "reference_antiderivative": "-5*exp(2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0553", "stage": "atomic", "k": 1, "integrand": "exp(2*x)", "integrand_latex": "e^{2 x}", "integrand_latex_integral": "\\int e^{2 x} \\, dx", "reference_antiderivative": "exp(2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0554", "stage": "atomic", "k": 1, "integrand": "exp(-8*x)", "integrand_latex": "e^{- 8 x}", "integrand_latex_integral": "\\int e^{- 8 x} \\, dx", "reference_antiderivative": "-exp(-8*x)/8", "category": "exponential", "variable": "x"}
{"id": "atom-0555", "stage": "atomic", "k": 1, "integrand": "5*exp(-13*x)", "integrand_latex": "5 e^{- 13 x}", "integrand_latex_integral": "\\int 5 e^{- 13 x} \\, dx", "reference_antiderivative": "-5*exp(-13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0556", "stage": "atomic", "k": 1, "integrand": "-4*exp(2*x)", "integrand_latex": "- 4 e^{2 x}", "integrand_latex_integral": "\\int - 4 e^{2 x} \\, dx", "reference_antiderivative": "-2*exp(2*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0557", "stage": "atomic", "k": 1, "integrand": "-2*exp(14*x)", "integrand_latex": "- 2 e^{14 x}", "integrand_latex_integral": "\\int - 2 e^{14 x} \\, dx", "reference_antiderivative": "-exp(14*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0558", "stage": "atomic", "k": 1, "integrand": "-4*exp(8*x)", "integrand_latex": "- 4 e^{8 x}", "integrand_latex_integral": "\\int - 4 e^{8 x} \\, dx", "reference_antiderivative": "-exp(8*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0559", "stage": "atomic", "k": 1, "integrand": "2*exp(14*x)", "integrand_latex": "2 e^{14 x}", "integrand_latex_integral": "\\int 2 e^{14 x} \\, dx", "reference_antiderivative": "exp(14*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0560", "stage": "atomic", "k": 1, "integrand": "4*exp(7*x)", "integrand_latex": "4 e^{7 x}", "integrand_latex_integral": "\\int 4 e^{7 x} \\, dx", "reference_antiderivative": "4*exp(7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0561", "stage": "atomic", "k": 1, "integrand": "-exp(-3*x)", "integrand_latex": "- e^{- 3 x}", "integrand_latex_integral": "\\int - e^{- 3 x} \\, dx", "reference_antiderivative": "exp(-3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0562", "stage": "atomic", "k": 1, "integrand": "-4*exp(10*x)", "integrand_latex": "- 4 e^{10 x}", "integrand_latex_integral": "\\int - 4 e^{10 x} \\, dx", "reference_antiderivative": "-2*exp(10*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0563", "stage": "atomic", "k": 1, "integrand": "-3*exp(-15*x)", "integrand_latex": "- 3 e^{- 15 x}", "integrand_latex_integral": "\\int - 3 e^{- 15 x} \\, dx", "reference_antiderivative": "exp(-15*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0564", "stage": "atomic", "k": 1, "integrand": "-2*exp(-3*x)", "integrand_latex": "- 2 e^{- 3 x}", "integrand_latex_integral": "\\int - 2 e^{- 3 x} \\, dx", "reference_antiderivative": "2*exp(-3*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0565", "stage": "atomic", "k": 1, "integrand": "5*exp(-5*x)", "integrand_latex": "5 e^{- 5 x}", "integrand_latex_integral": "\\int 5 e^{- 5 x} \\, dx", "reference_antiderivative": "-exp(-5*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0566", "stage": "atomic", "k": 1, "integrand": "2*exp(15*x)", "integrand_latex": "2 e^{15 x}", "integrand_latex_integral": "\\int 2 e^{15 x} \\, dx", "reference_antiderivative": "2*exp(15*x)/15", "category": "exponential", "variable": "x"}
{"id": "atom-0567", "stage": "atomic", "k": 1, "integrand": "-3*exp(-11*x)", "integrand_latex": "- 3 e^{- 11 x}", "integrand_latex_integral": "\\int - 3 e^{- 11 x} \\, dx", "reference_antiderivative": "3*exp(-11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0568", "stage": "atomic", "k": 1, "integrand": "-4*exp(15*x)", "integrand_latex": "- 4 e^{15 x}", "integrand_latex_integral": "\\int - 4 e^{15 x} \\, dx", "reference_antiderivative": "-4*exp(15*x)/15", "category": "exponential", "variable": "x"}
{"id": "atom-0569", "stage": "atomic", "k": 1, "integrand": "-2*exp(x)", "integrand_latex": "- 2 e^{x}", "integrand_latex_integral": "\\int - 2 e^{x} \\, dx", "reference_antiderivative": "-2*exp(x)", "category": "exponential", "variable": "x"}
{"id": "atom-0570", "stage": "atomic", "k": 1, "integrand": "-5*exp(4*x)", "integrand_latex": "- 5 e^{4 x}", "integrand_latex_integral": "\\int - 5 e^{4 x} \\, dx", "reference_antiderivative": "-5*exp(4*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0571", "stage": "atomic", "k": 1, "integrand": "3*exp(8*x)", "integrand_latex": "3 e^{8 x}", "integrand_latex_integral": "\\int 3 e^{8 x} \\, dx", "reference_antiderivative": "3*exp(8*x)/8", "category": "exponential", "variable": "x"}
{"id": "atom-0572", "stage": "atomic", "k": 1, "integrand": "5*exp(-2*x)", "integrand_latex": "5 e^{- 2 x}", "integrand_latex_integral": "\\int 5 e^{- 2 x} \\, dx", "reference_antiderivative": "-5*exp(-2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0573", "stage": "atomic", "k": 1, "integrand": "-3*exp(-12*x)", "integrand_latex": "- 3 e^{- 12 x}", "integrand_latex_integral": "\\int - 3 e^{- 12 x} \\, dx", "reference_antiderivative": "exp(-12*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0574", "stage": "atomic", "k": 1, "integrand": "4*exp(x)", "integrand_latex": "4 e^{x}", "integrand_latex_integral": "\\int 4 e^{x} \\, dx", "reference_antiderivative": "4*exp(x)", "category": "exponential", "variable": "x"}
{"id": "atom-0575", "stage": "atomic", "k": 1, "integrand": "-exp(10*x)", "integrand_latex": "- e^{10 x}", "integrand_latex_integral": "\\int - e^{10 x} \\, dx", "reference_antiderivative": "-exp(10*x)/10", "category": "exponential", "variable": "x"}
{"id": "atom-0576", "stage": "atomic", "k": 1, "integrand": "-2*exp(-6*x)", "integrand_latex": "- 2 e^{- 6 x}", "integrand_latex_integral": "\\int - 2 e^{- 6 x} \\, dx", "reference_antiderivative": "exp(-6*x)/3", "category": "exponential", "variable": "x"}
{"id": "atom-0577", "stage": "atomic", "k": 1, "integrand": "-4*exp(5*x)", "integrand_latex": "- 4 e^{5 x}", "integrand_latex_integral": "\\int - 4 e^{5 x} \\, dx", "reference_antiderivative": "-4*exp(5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0578", "stage": "atomic", "k": 1, "integrand": "2*exp(-14*x)", "integrand_latex": "2 e^{- 14 x}", "integrand_latex_integral": "\\int 2 e^{- 14 x} \\, dx", "reference_antiderivative": "-exp(-14*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0579", "stage": "atomic", "k": 1, "integrand": "-3*exp(-13*x)", "integrand_latex": "- 3 e^{- 13 x}", "integrand_latex_integral": "\\int - 3 e^{- 13 x} \\, dx", "reference_antiderivative": "3*exp(-13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0580", "stage": "atomic", "k": 1, "integrand": "exp(5*x)", "integrand_latex": "e^{5 x}", "integrand_latex_integral": "\\int e^{5 x} \\, dx", "reference_antiderivative": "exp(5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0581", "stage": "atomic", "k": 1, "integrand": "-2*exp(13*x)", "integrand_latex": "- 2 e^{13 x}", "integrand_latex_integral": "\\int - 2 e^{13 x} \\, dx", "reference_antiderivative": "-2*exp(13*x)/13", "category": "exponential", "variable": "x"}
{"id": "atom-0582", "stage": "atomic", "k": 1, "integrand": "4*exp(-7*x)", "integrand_latex": "4 e^{- 7 x}", "integrand_latex_integral": "\\int 4 e^{- 7 x} \\, dx", "reference_antiderivative": "-4*exp(-7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0583", "stage": "atomic", "k": 1, "integrand": "3*exp(3*x)", "integrand_latex": "3 e^{3 x}", "integrand_latex_integral": "\\int 3 e^{3 x} \\, dx", "reference_antiderivative": "exp(3*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0584", "stage": "atomic", "k": 1, "integrand": "-3*exp(14*x)", "integrand_latex": "- 3 e^{14 x}", "integrand_latex_integral": "\\int - 3 e^{14 x} \\, dx", "reference_antiderivative": "-3*exp(14*x)/14", "category": "exponential", "variable": "x"}
{"id": "atom-0585", "stage": "atomic", "k": 1, "integrand": "exp(14*x)", "integrand_latex": "e^{14 x}", "integrand_latex_integral": "\\int e^{14 x} \\, dx", "reference_antiderivative": "exp(14*x)/14", "category": "exponential", "variable": "x"}
{"id": "atom-0586", "stage": "atomic", "k": 1, "integrand": "-3*exp(3*x)", "integrand_latex": "- 3 e^{3 x}", "integrand_latex_integral": "\\int - 3 e^{3 x} \\, dx", "reference_antiderivative": "-exp(3*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0587", "stage": "atomic", "k": 1, "integrand": "exp(9*x)", "integrand_latex": "e^{9 x}", "integrand_latex_integral": "\\int e^{9 x} \\, dx", "reference_antiderivative": "exp(9*x)/9", "category": "exponential", "variable": "x"}
{"id": "atom-0588", "stage": "atomic", "k": 1, "integrand": "-4*exp(x)", "integrand_latex": "- 4 e^{x}", "integrand_latex_integral": "\\int - 4 e^{x} \\, dx", "reference_antiderivative": "-4*exp(x)", "category": "exponential", "variable": "x"}
{"id": "atom-0589", "stage": "atomic", "k": 1, "integrand": "-5*exp(-12*x)", "integrand_latex": "- 5 e^{- 12 x}", "integrand_latex_integral": "\\int - 5 e^{- 12 x} \\, dx", "reference_antiderivative": "5*exp(-12*x)/12", "category": "exponential", "variable": "x"}
{"id": "atom-0590", "stage": "atomic", "k": 1, "integrand": "-4*exp(-5*x)", "integrand_latex": "- 4 e^{- 5 x}", "integrand_latex_integral": "\\int - 4 e^{- 5 x} \\, dx", "reference_antiderivative": "4*exp(-5*x)/5", "category": "exponential", "variable": "x"}
{"id": "atom-0591", "stage": "atomic", "k": 1, "integrand": "4*exp(15*x)", "integrand_latex": "4 e^{15 x}", "integrand_latex_integral": "\\int 4 e^{15 x} \\, dx", "reference_antiderivative": "4*exp(15*x)/15", "category": "exponential", "variable": "x"}
{"id": "atom-0592", "stage": "atomic", "k": 1, "integrand": "-5*exp(5*x)", "integrand_latex": "- 5 e^{5 x}", "integrand_latex_integral": "\\int - 5 e^{5 x} \\, dx", "reference_antiderivative": "-exp(5*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0593", "stage": "atomic", "k": 1, "integrand": "exp(-2*x)", "integrand_latex": "e^{- 2 x}", "integrand_latex_integral": "\\int e^{- 2 x} \\, dx", "reference_antiderivative": "-exp(-2*x)/2", "category": "exponential", "variable": "x"}
{"id": "atom-0594", "stage": "atomic", "k": 1, "integrand": "exp(7*x)", "integrand_latex": "e^{7 x}", "integrand_latex_integral": "\\int e^{7 x} \\, dx", "reference_antiderivative": "exp(7*x)/7", "category": "exponential", "variable": "x"}
{"id": "atom-0595", "stage": "atomic", "k": 1, "integrand": "-exp(-12*x)", "integrand_latex": "- e^{- 12 x}", "integrand_latex_integral": "\\int - e^{- 12 x} \\, dx", "reference_antiderivative": "exp(-12*x)/12", "category": "exponential", "variable": "x"}
{"id": "atom-0596", "stage": "atomic", "k": 1, "integrand": "exp(-15*x)", "integrand_latex": "e^{- 15 x}", "integrand_latex_integral": "\\int e^{- 15 x} \\, dx", "reference_antiderivative": "-exp(-15*x)/15", "category": "exponential", "variable": "x"}
{"id": "atom-0597", "stage": "atomic", "k": 1, "integrand": "-2*exp(8*x)", "integrand_latex": "- 2 e^{8 x}", "integrand_latex_integral": "\\int - 2 e^{8 x} \\, dx", "reference_antiderivative": "-exp(8*x)/4", "category": "exponential", "variable": "x"}
{"id": "atom-0598", "stage": "atomic", "k": 1, "integrand": "4*exp(4*x)", "integrand_latex": "4 e^{4 x}", "integrand_latex_integral": "\\int 4 e^{4 x} \\, dx", "reference_antiderivative": "exp(4*x)", "category": "exponential", "variable": "x"}
{"id": "atom-0599", "stage": "atomic", "k": 1, "integrand": "-4*exp(-11*x)", "integrand_latex": "- 4 e^{- 11 x}", "integrand_latex_integral": "\\int - 4 e^{- 11 x} \\, dx", "reference_antiderivative": "4*exp(-11*x)/11", "category": "exponential", "variable": "x"}
{"id": "atom-0600", "stage": "atomic", "k": 1, "integrand": "4/(10 - 3*x)", "integrand_latex": "\\frac{4}{10 - 3 x}", "integrand_latex_integral": "\\int \\frac{4}{10 - 3 x} \\, dx", "reference_antiderivative": "-4*log(3*x - 10)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0601", "stage": "atomic", "k": 1, "integrand": "1/(11*x + 11)", "integrand_latex": "\\frac{1}{11 x + 11}", "integrand_latex_integral": "\\int \\frac{1}{11 x + 11} \\, dx", "reference_antiderivative": "log(11*x + 11)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0602", "stage": "atomic", "k": 1, "integrand": "-log(4 - 5*x)", "integrand_latex": "- \\log{\\left(4 - 5 x \\right)}", "integrand_latex_integral": "\\int - \\log{\\left(4 - 5 x \\right)} \\, dx", "reference_antiderivative": "-x*log(4 - 5*x) + x + 4*log(5*x - 4)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0603", "stage": "atomic", "k": 1, "integrand": "2*log(-5*x - 10)", "integrand_latex": "2 \\log{\\left(- 5 x - 10 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(- 5 x - 10 \\right)} \\, dx", "reference_antiderivative": "2*x*log(-5*x - 10) - 2*x + 4*log(x + 2)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0604", "stage": "atomic", "k": 1, "integrand": "-1/(8*x + 7)", "integrand_latex": "- \\frac{1}{8 x + 7}", "integrand_latex_integral": "\\int - \\frac{1}{8 x + 7} \\, dx", "reference_antiderivative": "-log(8*x + 7)/8", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0605", "stage": "atomic", "k": 1, "integrand": "log(11 - 7*x)", "integrand_latex": "\\log{\\left(11 - 7 x \\right)}", "integrand_latex_integral": "\\int \\log{\\left(11 - 7 x \\right)} \\, dx", "reference_antiderivative": "x*log(11 - 7*x) - x - 11*log(7*x - 11)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0606", "stage": "atomic", "k": 1, "integrand": "-4/(14*x + 3)", "integrand_latex": "- \\frac{4}{14 x + 3}", "integrand_latex_integral": "\\int - \\frac{4}{14 x + 3} \\, dx", "reference_antiderivative": "-2*log(14*x + 3)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0607", "stage": "atomic", "k": 1, "integrand": "5*log(9*x + 2)", "integrand_latex": "5 \\log{\\left(9 x + 2 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(9 x + 2 \\right)} \\, dx", "reference_antiderivative": "5*x*log(9*x + 2) - 5*x + 10*log(9*x + 2)/9", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0608", "stage": "atomic", "k": 1, "integrand": "-2/(10 - x)", "integrand_latex": "- \\frac{2}{10 - x}", "integrand_latex_integral": "\\int - \\frac{2}{10 - x} \\, dx", "reference_antiderivative": "2*log(x - 10)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0609", "stage": "atomic", "k": 1, "integrand": "log(6*x)", "integrand_latex": "\\log{\\left(6 x \\right)}", "integrand_latex_integral": "\\int \\log{\\left(6 x \\right)} \\, dx", "reference_antiderivative": "x*log(6*x) - x", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0610", "stage": "atomic", "k": 1, "integrand": "-2/(6 - 7*x)", "integrand_latex": "- \\frac{2}{6 - 7 x}", "integrand_latex_integral": "\\int - \\frac{2}{6 - 7 x} \\, dx", "reference_antiderivative": "2*log(7*x - 6)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0611", "stage": "atomic", "k": 1, "integrand": "1/(-13*x - 1)", "integrand_latex": "\\frac{1}{- 13 x - 1}", "integrand_latex_integral": "\\int \\frac{1}{- 13 x - 1} \\, dx", "reference_antiderivative": "-log(13*x + 1)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0612", "stage": "atomic", "k": 1, "integrand": "4/(2 - 3*x)", "integrand_latex": "\\frac{4}{2 - 3 x}", "integrand_latex_integral": "\\int \\frac{4}{2 - 3 x} \\, dx", "reference_antiderivative": "-4*log(3*x - 2)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0613", "stage": "atomic", "k": 1, "integrand": "3/(10 - 14*x)", "integrand_latex": "\\frac{3}{10 - 14 x}", "integrand_latex_integral": "\\int \\frac{3}{10 - 14 x} \\, dx", "reference_antiderivative": "-3*log(14*x - 10)/14", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0614", "stage": "atomic", "k": 1, "integrand": "-4*log(9*x - 8)", "integrand_latex": "- 4 \\log{\\left(9 x - 8 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(9 x - 8 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(9*x - 8) + 4*x + 32*log(9*x - 8)/9", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0615", "stage": "atomic", "k": 1, "integrand": "-3/(5*x + 4)", "integrand_latex": "- \\frac{3}{5 x + 4}", "integrand_latex_integral": "\\int - \\frac{3}{5 x + 4} \\, dx", "reference_antiderivative": "-3*log(5*x + 4)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0616", "stage": "atomic", "k": 1, "integrand": "1/(-12*x - 15)", "integrand_latex": "\\frac{1}{- 12 x - 15}", "integrand_latex_integral": "\\int \\frac{1}{- 12 x - 15} \\, dx", "reference_antiderivative": "-log(12*x + 15)/12", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0617", "stage": "atomic", "k": 1, "integrand": "3*log(8*x + 1)", "integrand_latex": "3 \\log{\\left(8 x + 1 \\right)}", "integrand_latex_integral": "\\int 3 \\log{\\left(8 x + 1 \\right)} \\, dx", "reference_antiderivative": "3*x*log(8*x + 1) - 3*x + 3*log(8*x + 1)/8", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0618", "stage": "atomic", "k": 1, "integrand": "2*log(-4*x - 3)", "integrand_latex": "2 \\log{\\left(- 4 x - 3 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(- 4 x - 3 \\right)} \\, dx", "reference_antiderivative": "2*x*log(-4*x - 3) - 2*x + 3*log(4*x + 3)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0619", "stage": "atomic", "k": 1, "integrand": "-5*log(-12*x - 6)", "integrand_latex": "- 5 \\log{\\left(- 12 x - 6 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(- 12 x - 6 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(-12*x - 6) + 5*x - 5*log(2*x + 1)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0620", "stage": "atomic", "k": 1, "integrand": "-4*log(11*x + 15)", "integrand_latex": "- 4 \\log{\\left(11 x + 15 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(11 x + 15 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(11*x + 15) + 4*x - 60*log(11*x + 15)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0621", "stage": "atomic", "k": 1, "integrand": "-1/(-5*x - 1)", "integrand_latex": "- \\frac{1}{- 5 x - 1}", "integrand_latex_integral": "\\int - \\frac{1}{- 5 x - 1} \\, dx", "reference_antiderivative": "log(5*x + 1)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0622", "stage": "atomic", "k": 1, "integrand": "2/(-12*x - 1)", "integrand_latex": "\\frac{2}{- 12 x - 1}", "integrand_latex_integral": "\\int \\frac{2}{- 12 x - 1} \\, dx", "reference_antiderivative": "-log(12*x + 1)/6", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0623", "stage": "atomic", "k": 1, "integrand": "-4/(-6*x - 14)", "integrand_latex": "- \\frac{4}{- 6 x - 14}", "integrand_latex_integral": "\\int - \\frac{4}{- 6 x - 14} \\, dx", "reference_antiderivative": "2*log(3*x + 7)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0624", "stage": "atomic", "k": 1, "integrand": "-5*log(12*x - 5)", "integrand_latex": "- 5 \\log{\\left(12 x - 5 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(12 x - 5 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(12*x - 5) + 5*x + 25*log(12*x - 5)/12", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0625", "stage": "atomic", "k": 1, "integrand": "-2*log(x - 10)", "integrand_latex": "- 2 \\log{\\left(x - 10 \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(x - 10 \\right)} \\, dx", "reference_antiderivative": "-2*x*log(x - 10) + 2*x + 20*log(x - 10)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0626", "stage": "atomic", "k": 1, "integrand": "3/(15 - 2*x)", "integrand_latex": "\\frac{3}{15 - 2 x}", "integrand_latex_integral": "\\int \\frac{3}{15 - 2 x} \\, dx", "reference_antiderivative": "-3*log(2*x - 15)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0627", "stage": "atomic", "k": 1, "integrand": "5/(-10*x - 10)", "integrand_latex": "\\frac{5}{- 10 x - 10}", "integrand_latex_integral": "\\int \\frac{5}{- 10 x - 10} \\, dx", "reference_antiderivative": "-log(2*x + 2)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0628", "stage": "atomic", "k": 1, "integrand": "1/(8 - 15*x)", "integrand_latex": "\\frac{1}{8 - 15 x}", "integrand_latex_integral": "\\int \\frac{1}{8 - 15 x} \\, dx", "reference_antiderivative": "-log(15*x - 8)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0629", "stage": "atomic", "k": 1, "integrand": "2*log(3*x - 2)", "integrand_latex": "2 \\log{\\left(3 x - 2 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(3 x - 2 \\right)} \\, dx", "reference_antiderivative": "2*x*log(3*x - 2) - 2*x - 4*log(3*x - 2)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0630", "stage": "atomic", "k": 1, "integrand": "-2*log(9 - 7*x)", "integrand_latex": "- 2 \\log{\\left(9 - 7 x \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(9 - 7 x \\right)} \\, dx", "reference_antiderivative": "-2*x*log(9 - 7*x) + 2*x + 18*log(7*x - 9)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0631", "stage": "atomic", "k": 1, "integrand": "4*log(10 - 12*x)", "integrand_latex": "4 \\log{\\left(10 - 12 x \\right)}", "integrand_latex_integral": "\\int 4 \\log{\\left(10 - 12 x \\right)} \\, dx", "reference_antiderivative": "4*x*log(10 - 12*x) - 4*x - 10*log(6*x - 5)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0632", "stage": "atomic", "k": 1, "integrand": "-2*log(-x - 12)", "integrand_latex": "- 2 \\log{\\left(- x - 12 \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(- x - 12 \\right)} \\, dx", "reference_antiderivative": "-2*x*log(-x - 12) + 2*x - 24*log(x + 12)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0633", "stage": "atomic", "k": 1, "integrand": "3/(15*x + 5)", "integrand_latex": "\\frac{3}{15 x + 5}", "integrand_latex_integral": "\\int \\frac{3}{15 x + 5} \\, dx", "reference_antiderivative": "log(15*x + 5)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0634", "stage": "atomic", "k": 1, "integrand": "4/(3 - 3*x)", "integrand_latex": "\\frac{4}{3 - 3 x}", "integrand_latex_integral": "\\int \\frac{4}{3 - 3 x} \\, dx", "reference_antiderivative": "-4*log(3*x - 3)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0635", "stage": "atomic", "k": 1, "integrand": "2/(4*x - 10)", "integrand_latex": "\\frac{2}{4 x - 10}", "integrand_latex_integral": "\\int \\frac{2}{4 x - 10} \\, dx", "reference_antiderivative": "log(2*x - 5)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0636", "stage": "atomic", "k": 1, "integrand": "4/(3*x - 13)", "integrand_latex": "\\frac{4}{3 x - 13}", "integrand_latex_integral": "\\int \\frac{4}{3 x - 13} \\, dx", "reference_antiderivative": "4*log(3*x - 13)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0637", "stage": "atomic", "k": 1, "integrand": "-4/(-8*x - 6)", "integrand_latex": "- \\frac{4}{- 8 x - 6}", "integrand_latex_integral": "\\int - \\frac{4}{- 8 x - 6} \\, dx", "reference_antiderivative": "log(4*x + 3)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0638", "stage": "atomic", "k": 1, "integrand": "-3/(x - 3)", "integrand_latex": "- \\frac{3}{x - 3}", "integrand_latex_integral": "\\int - \\frac{3}{x - 3} \\, dx", "reference_antiderivative": "-3*log(x - 3)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0639", "stage": "atomic", "k": 1, "integrand": "4*log(-3*x - 2)", "integrand_latex": "4 \\log{\\left(- 3 x - 2 \\right)}", "integrand_latex_integral": "\\int 4 \\log{\\left(- 3 x - 2 \\right)} \\, dx", "reference_antiderivative": "4*x*log(-3*x - 2) - 4*x + 8*log(3*x + 2)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0640", "stage": "atomic", "k": 1, "integrand": "3*log(-10*x)", "integrand_latex": "3 \\log{\\left(- 10 x \\right)}", "integrand_latex_integral": "\\int 3 \\log{\\left(- 10 x \\right)} \\, dx", "reference_antiderivative": "3*x*log(-10*x) - 3*x", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0641", "stage": "atomic", "k": 1, "integrand": "2*log(4*x - 14)", "integrand_latex": "2 \\log{\\left(4 x - 14 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(4 x - 14 \\right)} \\, dx", "reference_antiderivative": "2*x*log(4*x - 14) - 2*x - 7*log(2*x - 7)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0642", "stage": "atomic", "k": 1, "integrand": "2*log(-11*x - 9)", "integrand_latex": "2 \\log{\\left(- 11 x - 9 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(- 11 x - 9 \\right)} \\, dx", "reference_antiderivative": "2*x*log(-11*x - 9) - 2*x + 18*log(11*x + 9)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0643", "stage": "atomic", "k": 1, "integrand": "1/(6*x)", "integrand_latex": "\\frac{1}{6 x}", "integrand_latex_integral": "\\int \\frac{1}{6 x} \\, dx", "reference_antiderivative": "log(x)/6", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0644", "stage": "atomic", "k": 1, "integrand": "2/(-10*x - 13)", "integrand_latex": "\\frac{2}{- 10 x - 13}", "integrand_latex_integral": "\\int \\frac{2}{- 10 x - 13} \\, dx", "reference_antiderivative": "-log(10*x + 13)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0645", "stage": "atomic", "k": 1, "integrand": "-log(-14*x - 7)", "integrand_latex": "- \\log{\\left(- 14 x - 7 \\right)}", "integrand_latex_integral": "\\int - \\log{\\left(- 14 x - 7 \\right)} \\, dx", "reference_antiderivative": "-x*log(-14*x - 7) + x - log(2*x + 1)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0646", "stage": "atomic", "k": 1, "integrand": "-3/(9*x - 1)", "integrand_latex": "- \\frac{3}{9 x - 1}", "integrand_latex_integral": "\\int - \\frac{3}{9 x - 1} \\, dx", "reference_antiderivative": "-log(9*x - 1)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0647", "stage": "atomic", "k": 1, "integrand": "3/(x - 12)", "integrand_latex": "\\frac{3}{x - 12}", "integrand_latex_integral": "\\int \\frac{3}{x - 12} \\, dx", "reference_antiderivative": "3*log(x - 12)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0648", "stage": "atomic", "k": 1, "integrand": "3/(11*x - 4)", "integrand_latex": "\\frac{3}{11 x - 4}", "integrand_latex_integral": "\\int \\frac{3}{11 x - 4} \\, dx", "reference_antiderivative": "3*log(11*x - 4)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0649", "stage": "atomic", "k": 1, "integrand": "2*log(2*x - 9)", "integrand_latex": "2 \\log{\\left(2 x - 9 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(2 x - 9 \\right)} \\, dx", "reference_antiderivative": "2*x*log(2*x - 9) - 2*x - 9*log(2*x - 9)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0650", "stage": "atomic", "k": 1, "integrand": "5*log(9*x - 8)", "integrand_latex": "5 \\log{\\left(9 x - 8 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(9 x - 8 \\right)} \\, dx", "reference_antiderivative": "5*x*log(9*x - 8) - 5*x - 40*log(9*x - 8)/9", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0651", "stage": "atomic", "k": 1, "integrand": "2*log(-7*x - 4)", "integrand_latex": "2 \\log{\\left(- 7 x - 4 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(- 7 x - 4 \\right)} \\, dx", "reference_antiderivative": "2*x*log(-7*x - 4) - 2*x + 8*log(7*x + 4)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0652", "stage": "atomic", "k": 1, "integrand": "2*log(12*x - 12)", "integrand_latex": "2 \\log{\\left(12 x - 12 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(12 x - 12 \\right)} \\, dx", "reference_antiderivative": "2*x*log(12*x - 12) - 2*x - 2*log(x - 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0653", "stage": "atomic", "k": 1, "integrand": "-2*log(10*x + 8)", "integrand_latex": "- 2 \\log{\\left(10 x + 8 \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(10 x + 8 \\right)} \\, dx", "reference_antiderivative": "-2*x*log(10*x + 8) + 2*x - 8*log(5*x + 4)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0654", "stage": "atomic", "k": 1, "integrand": "4/(5*x - 2)", "integrand_latex": "\\frac{4}{5 x - 2}", "integrand_latex_integral": "\\int \\frac{4}{5 x - 2} \\, dx", "reference_antiderivative": "4*log(5*x - 2)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0655", "stage": "atomic", "k": 1, "integrand": "-2*log(11*x - 9)", "integrand_latex": "- 2 \\log{\\left(11 x - 9 \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(11 x - 9 \\right)} \\, dx", "reference_antiderivative": "-2*x*log(11*x - 9) + 2*x + 18*log(11*x - 9)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0656", "stage": "atomic", "k": 1, "integrand": "3/(4 - 7*x)", "integrand_latex": "\\frac{3}{4 - 7 x}", "integrand_latex_integral": "\\int \\frac{3}{4 - 7 x} \\, dx", "reference_antiderivative": "-3*log(7*x - 4)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0657", "stage": "atomic", "k": 1, "integrand": "-1/(3 - 6*x)", "integrand_latex": "- \\frac{1}{3 - 6 x}", "integrand_latex_integral": "\\int - \\frac{1}{3 - 6 x} \\, dx", "reference_antiderivative": "log(6*x - 3)/6", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0658", "stage": "atomic", "k": 1, "integrand": "-3*log(15*x + 9)", "integrand_latex": "- 3 \\log{\\left(15 x + 9 \\right)}", "integrand_latex_integral": "\\int - 3 \\log{\\left(15 x + 9 \\right)} \\, dx", "reference_antiderivative": "-3*x*log(15*x + 9) + 3*x - 9*log(5*x + 3)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0659", "stage": "atomic", "k": 1, "integrand": "-log(12*x + 5)", "integrand_latex": "- \\log{\\left(12 x + 5 \\right)}", "integrand_latex_integral": "\\int - \\log{\\left(12 x + 5 \\right)} \\, dx", "reference_antiderivative": "-x*log(12*x + 5) + x - 5*log(12*x + 5)/12", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0660", "stage": "atomic", "k": 1, "integrand": "-2*log(7 - 11*x)", "integrand_latex": "- 2 \\log{\\left(7 - 11 x \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(7 - 11 x \\right)} \\, dx", "reference_antiderivative": "-2*x*log(7 - 11*x) + 2*x + 14*log(11*x - 7)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0661", "stage": "atomic", "k": 1, "integrand": "5*log(-3*x)", "integrand_latex": "5 \\log{\\left(- 3 x \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(- 3 x \\right)} \\, dx", "reference_antiderivative": "5*x*log(-3*x) - 5*x", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0662", "stage": "atomic", "k": 1, "integrand": "5/(-2*x - 3)", "integrand_latex": "\\frac{5}{- 2 x - 3}", "integrand_latex_integral": "\\int \\frac{5}{- 2 x - 3} \\, dx", "reference_antiderivative": "-5*log(2*x + 3)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0663", "stage": "atomic", "k": 1, "integrand": "log(x + 8)", "integrand_latex": "\\log{\\left(x + 8 \\right)}", "integrand_latex_integral": "\\int \\log{\\left(x + 8 \\right)} \\, dx", "reference_antiderivative": "x*log(x + 8) - x + 8*log(x + 8)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0664", "stage": "atomic", "k": 1, "integrand": "2/(15*x)", "integrand_latex": "\\frac{2}{15 x}", "integrand_latex_integral": "\\int \\frac{2}{15 x} \\, dx", "reference_antiderivative": "2*log(x)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0665", "stage": "atomic", "k": 1, "integrand": "-4*log(8*x - 1)", "integrand_latex": "- 4 \\log{\\left(8 x - 1 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(8 x - 1 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(8*x - 1) + 4*x + log(8*x - 1)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0666", "stage": "atomic", "k": 1, "integrand": "-4/(10*x + 2)", "integrand_latex": "- \\frac{4}{10 x + 2}", "integrand_latex_integral": "\\int - \\frac{4}{10 x + 2} \\, dx", "reference_antiderivative": "-2*log(5*x + 1)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0667", "stage": "atomic", "k": 1, "integrand": "-2/(-7*x - 5)", "integrand_latex": "- \\frac{2}{- 7 x - 5}", "integrand_latex_integral": "\\int - \\frac{2}{- 7 x - 5} \\, dx", "reference_antiderivative": "2*log(7*x + 5)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0668", "stage": "atomic", "k": 1, "integrand": "3/(3*x - 11)", "integrand_latex": "\\frac{3}{3 x - 11}", "integrand_latex_integral": "\\int \\frac{3}{3 x - 11} \\, dx", "reference_antiderivative": "log(3*x - 11)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0669", "stage": "atomic", "k": 1, "integrand": "5/(9*x - 14)", "integrand_latex": "\\frac{5}{9 x - 14}", "integrand_latex_integral": "\\int \\frac{5}{9 x - 14} \\, dx", "reference_antiderivative": "5*log(9*x - 14)/9", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0670", "stage": "atomic", "k": 1, "integrand": "-5/(14 - 12*x)", "integrand_latex": "- \\frac{5}{14 - 12 x}", "integrand_latex_integral": "\\int - \\frac{5}{14 - 12 x} \\, dx", "reference_antiderivative": "5*log(12*x - 14)/12", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0671", "stage": "atomic", "k": 1, "integrand": "2/(15 - 15*x)", "integrand_latex": "\\frac{2}{15 - 15 x}", "integrand_latex_integral": "\\int \\frac{2}{15 - 15 x} \\, dx", "reference_antiderivative": "-2*log(15*x - 15)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0672", "stage": "atomic", "k": 1, "integrand": "5*log(-6*x - 10)", "integrand_latex": "5 \\log{\\left(- 6 x - 10 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(- 6 x - 10 \\right)} \\, dx", "reference_antiderivative": "5*x*log(-6*x - 10) - 5*x + 25*log(3*x + 5)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0673", "stage": "atomic", "k": 1, "integrand": "-4/(5*x - 4)", "integrand_latex": "- \\frac{4}{5 x - 4}", "integrand_latex_integral": "\\int - \\frac{4}{5 x - 4} \\, dx", "reference_antiderivative": "-4*log(5*x - 4)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0674", "stage": "atomic", "k": 1, "integrand": "5/(13*x + 5)", "integrand_latex": "\\frac{5}{13 x + 5}", "integrand_latex_integral": "\\int \\frac{5}{13 x + 5} \\, dx", "reference_antiderivative": "5*log(13*x + 5)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0675", "stage": "atomic", "k": 1, "integrand": "5/(8 - 6*x)", "integrand_latex": "\\frac{5}{8 - 6 x}", "integrand_latex_integral": "\\int \\frac{5}{8 - 6 x} \\, dx", "reference_antiderivative": "-5*log(6*x - 8)/6", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0676", "stage": "atomic", "k": 1, "integrand": "log(5*x - 13)", "integrand_latex": "\\log{\\left(5 x - 13 \\right)}", "integrand_latex_integral": "\\int \\log{\\left(5 x - 13 \\right)} \\, dx", "reference_antiderivative": "x*log(5*x - 13) - x - 13*log(5*x - 13)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0677", "stage": "atomic", "k": 1, "integrand": "-2*log(-13*x - 11)", "integrand_latex": "- 2 \\log{\\left(- 13 x - 11 \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(- 13 x - 11 \\right)} \\, dx", "reference_antiderivative": "-2*x*log(-13*x - 11) + 2*x - 22*log(13*x + 11)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0678", "stage": "atomic", "k": 1, "integrand": "-5/(7 - 15*x)", "integrand_latex": "- \\frac{5}{7 - 15 x}", "integrand_latex_integral": "\\int - \\frac{5}{7 - 15 x} \\, dx", "reference_antiderivative": "log(15*x - 7)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0679", "stage": "atomic", "k": 1, "integrand": "log(7*x - 11)", "integrand_latex": "\\log{\\left(7 x - 11 \\right)}", "integrand_latex_integral": "\\int \\log{\\left(7 x - 11 \\right)} \\, dx", "reference_antiderivative": "x*log(7*x - 11) - x - 11*log(7*x - 11)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0680", "stage": "atomic", "k": 1, "integrand": "log(8 - 13*x)", "integrand_latex": "\\log{\\left(8 - 13 x \\right)}", "integrand_latex_integral": "\\int \\log{\\left(8 - 13 x \\right)} \\, dx", "reference_antiderivative": "x*log(8 - 13*x) - x - 8*log(13*x - 8)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0681", "stage": "atomic", "k": 1, "integrand": "-log(-11*x - 3)", "integrand_latex": "- \\log{\\left(- 11 x - 3 \\right)}", "integrand_latex_integral": "\\int - \\log{\\left(- 11 x - 3 \\right)} \\, dx", "reference_antiderivative": "-x*log(-11*x - 3) + x - 3*log(11*x + 3)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0682", "stage": "atomic", "k": 1, "integrand": "5*log(6*x - 11)", "integrand_latex": "5 \\log{\\left(6 x - 11 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(6 x - 11 \\right)} \\, dx", "reference_antiderivative": "5*x*log(6*x - 11) - 5*x - 55*log(6*x - 11)/6", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0683", "stage": "atomic", "k": 1, "integrand": "4*log(5*x - 10)", "integrand_latex": "4 \\log{\\left(5 x - 10 \\right)}", "integrand_latex_integral": "\\int 4 \\log{\\left(5 x - 10 \\right)} \\, dx", "reference_antiderivative": "4*x*log(5*x - 10) - 4*x - 8*log(x - 2)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0684", "stage": "atomic", "k": 1, "integrand": "5*log(8*x - 11)", "integrand_latex": "5 \\log{\\left(8 x - 11 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(8 x - 11 \\right)} \\, dx", "reference_antiderivative": "5*x*log(8*x - 11) - 5*x - 55*log(8*x - 11)/8", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0685", "stage": "atomic", "k": 1, "integrand": "-2/(13 - 13*x)", "integrand_latex": "- \\frac{2}{13 - 13 x}", "integrand_latex_integral": "\\int - \\frac{2}{13 - 13 x} \\, dx", "reference_antiderivative": "2*log(13*x - 13)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0686", "stage": "atomic", "k": 1, "integrand": "4*log(8*x - 3)", "integrand_latex": "4 \\log{\\left(8 x - 3 \\right)}", "integrand_latex_integral": "\\int 4 \\log{\\left(8 x - 3 \\right)} \\, dx", "reference_antiderivative": "4*x*log(8*x - 3) - 4*x - 3*log(8*x - 3)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0687", "stage": "atomic", "k": 1, "integrand": "-3/(-8*x - 7)", "integrand_latex": "- \\frac{3}{- 8 x - 7}", "integrand_latex_integral": "\\int - \\frac{3}{- 8 x - 7} \\, dx", "reference_antiderivative": "3*log(8*x + 7)/8", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0688", "stage": "atomic", "k": 1, "integrand": "3*log(4*x + 4)", "integrand_latex": "3 \\log{\\left(4 x + 4 \\right)}", "integrand_latex_integral": "\\int 3 \\log{\\left(4 x + 4 \\right)} \\, dx", "reference_antiderivative": "3*x*log(4*x + 4) - 3*x + 3*log(x + 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0689", "stage": "atomic", "k": 1, "integrand": "-5/(12*x + 12)", "integrand_latex": "- \\frac{5}{12 x + 12}", "integrand_latex_integral": "\\int - \\frac{5}{12 x + 12} \\, dx", "reference_antiderivative": "-5*log(12*x + 12)/12", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0690", "stage": "atomic", "k": 1, "integrand": "-2/(x + 4)", "integrand_latex": "- \\frac{2}{x + 4}", "integrand_latex_integral": "\\int - \\frac{2}{x + 4} \\, dx", "reference_antiderivative": "-2*log(x + 4)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0691", "stage": "atomic", "k": 1, "integrand": "-1/(5*x - 14)", "integrand_latex": "- \\frac{1}{5 x - 14}", "integrand_latex_integral": "\\int - \\frac{1}{5 x - 14} \\, dx", "reference_antiderivative": "-log(5*x - 14)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0692", "stage": "atomic", "k": 1, "integrand": "2*log(-3*x - 12)", "integrand_latex": "2 \\log{\\left(- 3 x - 12 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(- 3 x - 12 \\right)} \\, dx", "reference_antiderivative": "2*x*log(-3*x - 12) - 2*x + 8*log(x + 4)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0693", "stage": "atomic", "k": 1, "integrand": "3*log(13*x - 15)", "integrand_latex": "3 \\log{\\left(13 x - 15 \\right)}", "integrand_latex_integral": "\\int 3 \\log{\\left(13 x - 15 \\right)} \\, dx", "reference_antiderivative": "3*x*log(13*x - 15) - 3*x - 45*log(13*x - 15)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0694", "stage": "atomic", "k": 1, "integrand": "-3/(12 - 3*x)", "integrand_latex": "- \\frac{3}{12 - 3 x}", "integrand_latex_integral": "\\int - \\frac{3}{12 - 3 x} \\, dx", "reference_antiderivative": "log(x - 4)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0695", "stage": "atomic", "k": 1, "integrand": "3/(6*x - 10)", "integrand_latex": "\\frac{3}{6 x - 10}", "integrand_latex_integral": "\\int \\frac{3}{6 x - 10} \\, dx", "reference_antiderivative": "log(6*x - 10)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0696", "stage": "atomic", "k": 1, "integrand": "-5*log(3*x - 13)", "integrand_latex": "- 5 \\log{\\left(3 x - 13 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(3 x - 13 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(3*x - 13) + 5*x + 65*log(3*x - 13)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0697", "stage": "atomic", "k": 1, "integrand": "-5*log(14*x - 14)", "integrand_latex": "- 5 \\log{\\left(14 x - 14 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(14 x - 14 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(14*x - 14) + 5*x + 5*log(x - 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0698", "stage": "atomic", "k": 1, "integrand": "3/(5 - 6*x)", "integrand_latex": "\\frac{3}{5 - 6 x}", "integrand_latex_integral": "\\int \\frac{3}{5 - 6 x} \\, dx", "reference_antiderivative": "-log(6*x - 5)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0699", "stage": "atomic", "k": 1, "integrand": "1/(7*x - 3)", "integrand_latex": "\\frac{1}{7 x - 3}", "integrand_latex_integral": "\\int \\frac{1}{7 x - 3} \\, dx", "reference_antiderivative": "log(7*x - 3)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0700", "stage": "atomic", "k": 1, "integrand": "-log(-13*x - 6)", "integrand_latex": "- \\log{\\left(- 13 x - 6 \\right)}", "integrand_latex_integral": "\\int - \\log{\\left(- 13 x - 6 \\right)} \\, dx", "reference_antiderivative": "-x*log(-13*x - 6) + x - 6*log(13*x + 6)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0701", "stage": "atomic", "k": 1, "integrand": "-3*log(2*x - 5)", "integrand_latex": "- 3 \\log{\\left(2 x - 5 \\right)}", "integrand_latex_integral": "\\int - 3 \\log{\\left(2 x - 5 \\right)} \\, dx", "reference_antiderivative": "-3*x*log(2*x - 5) + 3*x + 15*log(2*x - 5)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0702", "stage": "atomic", "k": 1, "integrand": "-log(7*x - 2)", "integrand_latex": "- \\log{\\left(7 x - 2 \\right)}", "integrand_latex_integral": "\\int - \\log{\\left(7 x - 2 \\right)} \\, dx", "reference_antiderivative": "-x*log(7*x - 2) + x + 2*log(7*x - 2)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0703", "stage": "atomic", "k": 1, "integrand": "-5*log(-8*x - 13)", "integrand_latex": "- 5 \\log{\\left(- 8 x - 13 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(- 8 x - 13 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(-8*x - 13) + 5*x - 65*log(8*x + 13)/8", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0704", "stage": "atomic", "k": 1, "integrand": "2*log(4*x + 4)", "integrand_latex": "2 \\log{\\left(4 x + 4 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(4 x + 4 \\right)} \\, dx", "reference_antiderivative": "2*x*log(4*x + 4) - 2*x + 2*log(x + 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0705", "stage": "atomic", "k": 1, "integrand": "-4*log(7 - 15*x)", "integrand_latex": "- 4 \\log{\\left(7 - 15 x \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(7 - 15 x \\right)} \\, dx", "reference_antiderivative": "-4*x*log(7 - 15*x) + 4*x + 28*log(15*x - 7)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0706", "stage": "atomic", "k": 1, "integrand": "-3*log(15*x - 4)", "integrand_latex": "- 3 \\log{\\left(15 x - 4 \\right)}", "integrand_latex_integral": "\\int - 3 \\log{\\left(15 x - 4 \\right)} \\, dx", "reference_antiderivative": "-3*x*log(15*x - 4) + 3*x + 4*log(15*x - 4)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0707", "stage": "atomic", "k": 1, "integrand": "-3/(-4*x - 11)", "integrand_latex": "- \\frac{3}{- 4 x - 11}", "integrand_latex_integral": "\\int - \\frac{3}{- 4 x - 11} \\, dx", "reference_antiderivative": "3*log(4*x + 11)/4", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0708", "stage": "atomic", "k": 1, "integrand": "-4/(9*x + 13)", "integrand_latex": "- \\frac{4}{9 x + 13}", "integrand_latex_integral": "\\int - \\frac{4}{9 x + 13} \\, dx", "reference_antiderivative": "-4*log(9*x + 13)/9", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0709", "stage": "atomic", "k": 1, "integrand": "-1/(x - 13)", "integrand_latex": "- \\frac{1}{x - 13}", "integrand_latex_integral": "\\int - \\frac{1}{x - 13} \\, dx", "reference_antiderivative": "-log(x - 13)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0710", "stage": "atomic", "k": 1, "integrand": "2*log(1 - x)", "integrand_latex": "2 \\log{\\left(1 - x \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(1 - x \\right)} \\, dx", "reference_antiderivative": "2*x*log(1 - x) - 2*x - 2*log(x - 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0711", "stage": "atomic", "k": 1, "integrand": "4/(-10*x - 4)", "integrand_latex": "\\frac{4}{- 10 x - 4}", "integrand_latex_integral": "\\int \\frac{4}{- 10 x - 4} \\, dx", "reference_antiderivative": "-2*log(5*x + 2)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0712", "stage": "atomic", "k": 1, "integrand": "4*log(6*x + 8)", "integrand_latex": "4 \\log{\\left(6 x + 8 \\right)}", "integrand_latex_integral": "\\int 4 \\log{\\left(6 x + 8 \\right)} \\, dx", "reference_antiderivative": "4*x*log(6*x + 8) - 4*x + 16*log(3*x + 4)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0713", "stage": "atomic", "k": 1, "integrand": "-5*log(12*x + 12)", "integrand_latex": "- 5 \\log{\\left(12 x + 12 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(12 x + 12 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(12*x + 12) + 5*x - 5*log(x + 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0714", "stage": "atomic", "k": 1, "integrand": "-5*log(2*x + 10)", "integrand_latex": "- 5 \\log{\\left(2 x + 10 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(2 x + 10 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(2*x + 10) + 5*x - 25*log(x + 5)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0715", "stage": "atomic", "k": 1, "integrand": "-2/(-5*x - 8)", "integrand_latex": "- \\frac{2}{- 5 x - 8}", "integrand_latex_integral": "\\int - \\frac{2}{- 5 x - 8} \\, dx", "reference_antiderivative": "2*log(5*x + 8)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0716", "stage": "atomic", "k": 1, "integrand": "-1/(11*x - 13)", "integrand_latex": "- \\frac{1}{11 x - 13}", "integrand_latex_integral": "\\int - \\frac{1}{11 x - 13} \\, dx", "reference_antiderivative": "-log(11*x - 13)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0717", "stage": "atomic", "k": 1, "integrand": "3*log(6*x + 13)", "integrand_latex": "3 \\log{\\left(6 x + 13 \\right)}", "integrand_latex_integral": "\\int 3 \\log{\\left(6 x + 13 \\right)} \\, dx", "reference_antiderivative": "3*x*log(6*x + 13) - 3*x + 13*log(6*x + 13)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0718", "stage": "atomic", "k": 1, "integrand": "3*log(15 - 14*x)", "integrand_latex": "3 \\log{\\left(15 - 14 x \\right)}", "integrand_latex_integral": "\\int 3 \\log{\\left(15 - 14 x \\right)} \\, dx", "reference_antiderivative": "3*x*log(15 - 14*x) - 3*x - 45*log(14*x - 15)/14", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0719", "stage": "atomic", "k": 1, "integrand": "-1/(9*x + 12)", "integrand_latex": "- \\frac{1}{9 x + 12}", "integrand_latex_integral": "\\int - \\frac{1}{9 x + 12} \\, dx", "reference_antiderivative": "-log(9*x + 12)/9", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0720", "stage": "atomic", "k": 1, "integrand": "3*log(-x - 15)", "integrand_latex": "3 \\log{\\left(- x - 15 \\right)}", "integrand_latex_integral": "\\int 3 \\log{\\left(- x - 15 \\right)} \\, dx", "reference_antiderivative": "3*x*log(-x - 15) - 3*x + 45*log(x + 15)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0721", "stage": "atomic", "k": 1, "integrand": "4/(10*x - 6)", "integrand_latex": "\\frac{4}{10 x - 6}", "integrand_latex_integral": "\\int \\frac{4}{10 x - 6} \\, dx", "reference_antiderivative": "2*log(5*x - 3)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0722", "stage": "atomic", "k": 1, "integrand": "2*log(3 - 4*x)", "integrand_latex": "2 \\log{\\left(3 - 4 x \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(3 - 4 x \\right)} \\, dx", "reference_antiderivative": "2*x*log(3 - 4*x) - 2*x - 3*log(4*x - 3)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0723", "stage": "atomic", "k": 1, "integrand": "3*log(9*x + 10)", "integrand_latex": "3 \\log{\\left(9 x + 10 \\right)}", "integrand_latex_integral": "\\int 3 \\log{\\left(9 x + 10 \\right)} \\, dx", "reference_antiderivative": "3*x*log(9*x + 10) - 3*x + 10*log(9*x + 10)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0724", "stage": "atomic", "k": 1, "integrand": "log(-15*x - 8)", "integrand_latex": "\\log{\\left(- 15 x - 8 \\right)}", "integrand_latex_integral": "\\int \\log{\\left(- 15 x - 8 \\right)} \\, dx", "reference_antiderivative": "x*log(-15*x - 8) - x + 8*log(15*x + 8)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0725", "stage": "atomic", "k": 1, "integrand": "-5*log(9*x + 6)", "integrand_latex": "- 5 \\log{\\left(9 x + 6 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(9 x + 6 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(9*x + 6) + 5*x - 10*log(3*x + 2)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0726", "stage": "atomic", "k": 1, "integrand": "-4/(1 - 9*x)", "integrand_latex": "- \\frac{4}{1 - 9 x}", "integrand_latex_integral": "\\int - \\frac{4}{1 - 9 x} \\, dx", "reference_antiderivative": "4*log(9*x - 1)/9", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0727", "stage": "atomic", "k": 1, "integrand": "2/(15*x - 14)", "integrand_latex": "\\frac{2}{15 x - 14}", "integrand_latex_integral": "\\int \\frac{2}{15 x - 14} \\, dx", "reference_antiderivative": "2*log(15*x - 14)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0728", "stage": "atomic", "k": 1, "integrand": "-log(-13*x - 14)", "integrand_latex": "- \\log{\\left(- 13 x - 14 \\right)}", "integrand_latex_integral": "\\int - \\log{\\left(- 13 x - 14 \\right)} \\, dx", "reference_antiderivative": "-x*log(-13*x - 14) + x - 14*log(13*x + 14)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0729", "stage": "atomic", "k": 1, "integrand": "2/(8*x - 13)", "integrand_latex": "\\frac{2}{8 x - 13}", "integrand_latex_integral": "\\int \\frac{2}{8 x - 13} \\, dx", "reference_antiderivative": "log(8*x - 13)/4", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0730", "stage": "atomic", "k": 1, "integrand": "5*log(11*x - 3)", "integrand_latex": "5 \\log{\\left(11 x - 3 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(11 x - 3 \\right)} \\, dx", "reference_antiderivative": "5*x*log(11*x - 3) - 5*x - 15*log(11*x - 3)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0731", "stage": "atomic", "k": 1, "integrand": "log(6*x + 15)", "integrand_latex": "\\log{\\left(6 x + 15 \\right)}", "integrand_latex_integral": "\\int \\log{\\left(6 x + 15 \\right)} \\, dx", "reference_antiderivative": "x*log(6*x + 15) - x + 5*log(2*x + 5)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0732", "stage": "atomic", "k": 1, "integrand": "-1/(12*x - 5)", "integrand_latex": "- \\frac{1}{12 x - 5}", "integrand_latex_integral": "\\int - \\frac{1}{12 x - 5} \\, dx", "reference_antiderivative": "-log(12*x - 5)/12", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0733", "stage": "atomic", "k": 1, "integrand": "2/(-7*x - 8)", "integrand_latex": "\\frac{2}{- 7 x - 8}", "integrand_latex_integral": "\\int \\frac{2}{- 7 x - 8} \\, dx", "reference_antiderivative": "-2*log(7*x + 8)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0734", "stage": "atomic", "k": 1, "integrand": "-3*log(9*x + 9)", "integrand_latex": "- 3 \\log{\\left(9 x + 9 \\right)}", "integrand_latex_integral": "\\int - 3 \\log{\\left(9 x + 9 \\right)} \\, dx", "reference_antiderivative": "-3*x*log(9*x + 9) + 3*x - 3*log(x + 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0735", "stage": "atomic", "k": 1, "integrand": "-4*log(-10*x - 1)", "integrand_latex": "- 4 \\log{\\left(- 10 x - 1 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(- 10 x - 1 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(-10*x - 1) + 4*x - 2*log(10*x + 1)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0736", "stage": "atomic", "k": 1, "integrand": "-4/(2*x - 4)", "integrand_latex": "- \\frac{4}{2 x - 4}", "integrand_latex_integral": "\\int - \\frac{4}{2 x - 4} \\, dx", "reference_antiderivative": "-2*log(x - 2)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0737", "stage": "atomic", "k": 1, "integrand": "2*log(-6*x - 1)", "integrand_latex": "2 \\log{\\left(- 6 x - 1 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(- 6 x - 1 \\right)} \\, dx", "reference_antiderivative": "2*x*log(-6*x - 1) - 2*x + log(6*x + 1)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0738", "stage": "atomic", "k": 1, "integrand": "-4*log(10 - 10*x)", "integrand_latex": "- 4 \\log{\\left(10 - 10 x \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(10 - 10 x \\right)} \\, dx", "reference_antiderivative": "-4*x*log(10 - 10*x) + 4*x + 4*log(x - 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0739", "stage": "atomic", "k": 1, "integrand": "-2*log(11*x + 12)", "integrand_latex": "- 2 \\log{\\left(11 x + 12 \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(11 x + 12 \\right)} \\, dx", "reference_antiderivative": "-2*x*log(11*x + 12) + 2*x - 24*log(11*x + 12)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0740", "stage": "atomic", "k": 1, "integrand": "-2*log(15*x - 4)", "integrand_latex": "- 2 \\log{\\left(15 x - 4 \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(15 x - 4 \\right)} \\, dx", "reference_antiderivative": "-2*x*log(15*x - 4) + 2*x + 8*log(15*x - 4)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0741", "stage": "atomic", "k": 1, "integrand": "5*log(-6*x - 7)", "integrand_latex": "5 \\log{\\left(- 6 x - 7 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(- 6 x - 7 \\right)} \\, dx", "reference_antiderivative": "5*x*log(-6*x - 7) - 5*x + 35*log(6*x + 7)/6", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0742", "stage": "atomic", "k": 1, "integrand": "-5*log(15*x - 3)", "integrand_latex": "- 5 \\log{\\left(15 x - 3 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(15 x - 3 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(15*x - 3) + 5*x + log(5*x - 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0743", "stage": "atomic", "k": 1, "integrand": "-4*log(-x - 12)", "integrand_latex": "- 4 \\log{\\left(- x - 12 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(- x - 12 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(-x - 12) + 4*x - 48*log(x + 12)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0744", "stage": "atomic", "k": 1, "integrand": "-4*log(-15*x - 14)", "integrand_latex": "- 4 \\log{\\left(- 15 x - 14 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(- 15 x - 14 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(-15*x - 14) + 4*x - 56*log(15*x + 14)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0745", "stage": "atomic", "k": 1, "integrand": "-3*log(11 - 9*x)", "integrand_latex": "- 3 \\log{\\left(11 - 9 x \\right)}", "integrand_latex_integral": "\\int - 3 \\log{\\left(11 - 9 x \\right)} \\, dx", "reference_antiderivative": "-3*x*log(11 - 9*x) + 3*x + 11*log(9*x - 11)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0746", "stage": "atomic", "k": 1, "integrand": "4*log(3*x - 7)", "integrand_latex": "4 \\log{\\left(3 x - 7 \\right)}", "integrand_latex_integral": "\\int 4 \\log{\\left(3 x - 7 \\right)} \\, dx", "reference_antiderivative": "4*x*log(3*x - 7) - 4*x - 28*log(3*x - 7)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0747", "stage": "atomic", "k": 1, "integrand": "-5*log(-13*x - 9)", "integrand_latex": "- 5 \\log{\\left(- 13 x - 9 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(- 13 x - 9 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(-13*x - 9) + 5*x - 45*log(13*x + 9)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0748", "stage": "atomic", "k": 1, "integrand": "-3/(13 - 13*x)", "integrand_latex": "- \\frac{3}{13 - 13 x}", "integrand_latex_integral": "\\int - \\frac{3}{13 - 13 x} \\, dx", "reference_antiderivative": "3*log(13*x - 13)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0749", "stage": "atomic", "k": 1, "integrand": "-4/(15 - 14*x)", "integrand_latex": "- \\frac{4}{15 - 14 x}", "integrand_latex_integral": "\\int - \\frac{4}{15 - 14 x} \\, dx", "reference_antiderivative": "2*log(14*x - 15)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0750", "stage": "atomic", "k": 1, "integrand": "4*log(11 - 2*x)", "integrand_latex": "4 \\log{\\left(11 - 2 x \\right)}", "integrand_latex_integral": "\\int 4 \\log{\\left(11 - 2 x \\right)} \\, dx", "reference_antiderivative": "4*x*log(11 - 2*x) - 4*x - 22*log(2*x - 11)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0751", "stage": "atomic", "k": 1, "integrand": "-5/(6 - 3*x)", "integrand_latex": "- \\frac{5}{6 - 3 x}", "integrand_latex_integral": "\\int - \\frac{5}{6 - 3 x} \\, dx", "reference_antiderivative": "5*log(3*x - 6)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0752", "stage": "atomic", "k": 1, "integrand": "-2/(14*x - 10)", "integrand_latex": "- \\frac{2}{14 x - 10}", "integrand_latex_integral": "\\int - \\frac{2}{14 x - 10} \\, dx", "reference_antiderivative": "-log(7*x - 5)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0753", "stage": "atomic", "k": 1, "integrand": "-3/(4 - 14*x)", "integrand_latex": "- \\frac{3}{4 - 14 x}", "integrand_latex_integral": "\\int - \\frac{3}{4 - 14 x} \\, dx", "reference_antiderivative": "3*log(14*x - 4)/14", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0754", "stage": "atomic", "k": 1, "integrand": "5*log(-6*x)", "integrand_latex": "5 \\log{\\left(- 6 x \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(- 6 x \\right)} \\, dx", "reference_antiderivative": "5*x*log(-6*x) - 5*x", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0755", "stage": "atomic", "k": 1, "integrand": "-5/(-13*x - 7)", "integrand_latex": "- \\frac{5}{- 13 x - 7}", "integrand_latex_integral": "\\int - \\frac{5}{- 13 x - 7} \\, dx", "reference_antiderivative": "5*log(13*x + 7)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0756", "stage": "atomic", "k": 1, "integrand": "-2/(5*x + 13)", "integrand_latex": "- \\frac{2}{5 x + 13}", "integrand_latex_integral": "\\int - \\frac{2}{5 x + 13} \\, dx", "reference_antiderivative": "-2*log(5*x + 13)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0757", "stage": "atomic", "k": 1, "integrand": "5*log(10*x + 2)", "integrand_latex": "5 \\log{\\left(10 x + 2 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(10 x + 2 \\right)} \\, dx", "reference_antiderivative": "5*x*log(10*x + 2) - 5*x + log(5*x + 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0758", "stage": "atomic", "k": 1, "integrand": "2/(2*x + 10)", "integrand_latex": "\\frac{2}{2 x + 10}", "integrand_latex_integral": "\\int \\frac{2}{2 x + 10} \\, dx", "reference_antiderivative": "log(x + 5)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0759", "stage": "atomic", "k": 1, "integrand": "1/(-7*x - 10)", "integrand_latex": "\\frac{1}{- 7 x - 10}", "integrand_latex_integral": "\\int \\frac{1}{- 7 x - 10} \\, dx", "reference_antiderivative": "-log(7*x + 10)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0760", "stage": "atomic", "k": 1, "integrand": "-5*log(13*x + 10)", "integrand_latex": "- 5 \\log{\\left(13 x + 10 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(13 x + 10 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(13*x + 10) + 5*x - 50*log(13*x + 10)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0761", "stage": "atomic", "k": 1, "integrand": "2*log(x - 4)", "integrand_latex": "2 \\log{\\left(x - 4 \\right)}", "integrand_latex_integral": "\\int 2 \\log{\\left(x - 4 \\right)} \\, dx", "reference_antiderivative": "2*x*log(x - 4) - 2*x - 8*log(x - 4)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0762", "stage": "atomic", "k": 1, "integrand": "-3*log(-12*x - 8)", "integrand_latex": "- 3 \\log{\\left(- 12 x - 8 \\right)}", "integrand_latex_integral": "\\int - 3 \\log{\\left(- 12 x - 8 \\right)} \\, dx", "reference_antiderivative": "-3*x*log(-12*x - 8) + 3*x - 2*log(3*x + 2)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0763", "stage": "atomic", "k": 1, "integrand": "3/(11*x + 10)", "integrand_latex": "\\frac{3}{11 x + 10}", "integrand_latex_integral": "\\int \\frac{3}{11 x + 10} \\, dx", "reference_antiderivative": "3*log(11*x + 10)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0764", "stage": "atomic", "k": 1, "integrand": "-2*log(3*x + 12)", "integrand_latex": "- 2 \\log{\\left(3 x + 12 \\right)}", "integrand_latex_integral": "\\int - 2 \\log{\\left(3 x + 12 \\right)} \\, dx", "reference_antiderivative": "-2*x*log(3*x + 12) + 2*x - 8*log(x + 4)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0765", "stage": "atomic", "k": 1, "integrand": "-3/(-10*x - 8)", "integrand_latex": "- \\frac{3}{- 10 x - 8}", "integrand_latex_integral": "\\int - \\frac{3}{- 10 x - 8} \\, dx", "reference_antiderivative": "3*log(10*x + 8)/10", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0766", "stage": "atomic", "k": 1, "integrand": "4/(7 - 15*x)", "integrand_latex": "\\frac{4}{7 - 15 x}", "integrand_latex_integral": "\\int \\frac{4}{7 - 15 x} \\, dx", "reference_antiderivative": "-4*log(15*x - 7)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0767", "stage": "atomic", "k": 1, "integrand": "4*log(15*x - 9)", "integrand_latex": "4 \\log{\\left(15 x - 9 \\right)}", "integrand_latex_integral": "\\int 4 \\log{\\left(15 x - 9 \\right)} \\, dx", "reference_antiderivative": "4*x*log(15*x - 9) - 4*x - 12*log(5*x - 3)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0768", "stage": "atomic", "k": 1, "integrand": "3/(-6*x - 10)", "integrand_latex": "\\frac{3}{- 6 x - 10}", "integrand_latex_integral": "\\int \\frac{3}{- 6 x - 10} \\, dx", "reference_antiderivative": "-log(6*x + 10)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0769", "stage": "atomic", "k": 1, "integrand": "-5*log(4 - 8*x)", "integrand_latex": "- 5 \\log{\\left(4 - 8 x \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(4 - 8 x \\right)} \\, dx", "reference_antiderivative": "-5*x*log(4 - 8*x) + 5*x + 5*log(2*x - 1)/2", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0770", "stage": "atomic", "k": 1, "integrand": "-5/(14 - 5*x)", "integrand_latex": "- \\frac{5}{14 - 5 x}", "integrand_latex_integral": "\\int - \\frac{5}{14 - 5 x} \\, dx", "reference_antiderivative": "log(5*x - 14)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0771", "stage": "atomic", "k": 1, "integrand": "-3*log(14*x + 10)", "integrand_latex": "- 3 \\log{\\left(14 x + 10 \\right)}", "integrand_latex_integral": "\\int - 3 \\log{\\left(14 x + 10 \\right)} \\, dx", "reference_antiderivative": "-3*x*log(14*x + 10) + 3*x - 15*log(7*x + 5)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0772", "stage": "atomic", "k": 1, "integrand": "-5/(-15*x - 11)", "integrand_latex": "- \\frac{5}{- 15 x - 11}", "integrand_latex_integral": "\\int - \\frac{5}{- 15 x - 11} \\, dx", "reference_antiderivative": "log(15*x + 11)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0773", "stage": "atomic", "k": 1, "integrand": "-4*log(12*x + 1)", "integrand_latex": "- 4 \\log{\\left(12 x + 1 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(12 x + 1 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(12*x + 1) + 4*x - log(12*x + 1)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0774", "stage": "atomic", "k": 1, "integrand": "5*log(3 - 3*x)", "integrand_latex": "5 \\log{\\left(3 - 3 x \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(3 - 3 x \\right)} \\, dx", "reference_antiderivative": "5*x*log(3 - 3*x) - 5*x - 5*log(x - 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0775", "stage": "atomic", "k": 1, "integrand": "-3/(8 - 10*x)", "integrand_latex": "- \\frac{3}{8 - 10 x}", "integrand_latex_integral": "\\int - \\frac{3}{8 - 10 x} \\, dx", "reference_antiderivative": "3*log(10*x - 8)/10", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0776", "stage": "atomic", "k": 1, "integrand": "5/(-5*x - 10)", "integrand_latex": "\\frac{5}{- 5 x - 10}", "integrand_latex_integral": "\\int \\frac{5}{- 5 x - 10} \\, dx", "reference_antiderivative": "-log(x + 2)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0777", "stage": "atomic", "k": 1, "integrand": "-2/(6*x + 3)", "integrand_latex": "- \\frac{2}{6 x + 3}", "integrand_latex_integral": "\\int - \\frac{2}{6 x + 3} \\, dx", "reference_antiderivative": "-log(6*x + 3)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0778", "stage": "atomic", "k": 1, "integrand": "-5*log(15*x + 7)", "integrand_latex": "- 5 \\log{\\left(15 x + 7 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(15 x + 7 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(15*x + 7) + 5*x - 7*log(15*x + 7)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0779", "stage": "atomic", "k": 1, "integrand": "4/(-14*x - 10)", "integrand_latex": "\\frac{4}{- 14 x - 10}", "integrand_latex_integral": "\\int \\frac{4}{- 14 x - 10} \\, dx", "reference_antiderivative": "-2*log(7*x + 5)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0780", "stage": "atomic", "k": 1, "integrand": "5*log(3*x - 12)", "integrand_latex": "5 \\log{\\left(3 x - 12 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(3 x - 12 \\right)} \\, dx", "reference_antiderivative": "5*x*log(3*x - 12) - 5*x - 20*log(x - 4)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0781", "stage": "atomic", "k": 1, "integrand": "-4*log(-8*x - 4)", "integrand_latex": "- 4 \\log{\\left(- 8 x - 4 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(- 8 x - 4 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(-8*x - 4) + 4*x - 2*log(2*x + 1)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0782", "stage": "atomic", "k": 1, "integrand": "5*log(13*x + 15)", "integrand_latex": "5 \\log{\\left(13 x + 15 \\right)}", "integrand_latex_integral": "\\int 5 \\log{\\left(13 x + 15 \\right)} \\, dx", "reference_antiderivative": "5*x*log(13*x + 15) - 5*x + 75*log(13*x + 15)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0783", "stage": "atomic", "k": 1, "integrand": "2/(-15*x - 7)", "integrand_latex": "\\frac{2}{- 15 x - 7}", "integrand_latex_integral": "\\int \\frac{2}{- 15 x - 7} \\, dx", "reference_antiderivative": "-2*log(15*x + 7)/15", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0784", "stage": "atomic", "k": 1, "integrand": "-log(10*x - 12)", "integrand_latex": "- \\log{\\left(10 x - 12 \\right)}", "integrand_latex_integral": "\\int - \\log{\\left(10 x - 12 \\right)} \\, dx", "reference_antiderivative": "-x*log(10*x - 12) + x + 6*log(5*x - 6)/5", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0785", "stage": "atomic", "k": 1, "integrand": "log(8 - x)", "integrand_latex": "\\log{\\left(8 - x \\right)}", "integrand_latex_integral": "\\int \\log{\\left(8 - x \\right)} \\, dx", "reference_antiderivative": "x*log(8 - x) - x - 8*log(x - 8)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0786", "stage": "atomic", "k": 1, "integrand": "log(13*x - 3)", "integrand_latex": "\\log{\\left(13 x - 3 \\right)}", "integrand_latex_integral": "\\int \\log{\\left(13 x - 3 \\right)} \\, dx", "reference_antiderivative": "x*log(13*x - 3) - x - 3*log(13*x - 3)/13", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0787", "stage": "atomic", "k": 1, "integrand": "-4/(11*x)", "integrand_latex": "- \\frac{4}{11 x}", "integrand_latex_integral": "\\int - \\frac{4}{11 x} \\, dx", "reference_antiderivative": "-4*log(x)/11", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0788", "stage": "atomic", "k": 1, "integrand": "-3*log(-x - 13)", "integrand_latex": "- 3 \\log{\\left(- x - 13 \\right)}", "integrand_latex_integral": "\\int - 3 \\log{\\left(- x - 13 \\right)} \\, dx", "reference_antiderivative": "-3*x*log(-x - 13) + 3*x - 39*log(x + 13)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0789", "stage": "atomic", "k": 1, "integrand": "-log(-15*x - 5)", "integrand_latex": "- \\log{\\left(- 15 x - 5 \\right)}", "integrand_latex_integral": "\\int - \\log{\\left(- 15 x - 5 \\right)} \\, dx", "reference_antiderivative": "-x*log(-15*x - 5) + x - log(3*x + 1)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0790", "stage": "atomic", "k": 1, "integrand": "-4*log(-5*x - 10)", "integrand_latex": "- 4 \\log{\\left(- 5 x - 10 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(- 5 x - 10 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(-5*x - 10) + 4*x - 8*log(x + 2)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0791", "stage": "atomic", "k": 1, "integrand": "-4*log(2*x + 15)", "integrand_latex": "- 4 \\log{\\left(2 x + 15 \\right)}", "integrand_latex_integral": "\\int - 4 \\log{\\left(2 x + 15 \\right)} \\, dx", "reference_antiderivative": "-4*x*log(2*x + 15) + 4*x - 30*log(2*x + 15)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0792", "stage": "atomic", "k": 1, "integrand": "4*log(4*x + 13)", "integrand_latex": "4 \\log{\\left(4 x + 13 \\right)}", "integrand_latex_integral": "\\int 4 \\log{\\left(4 x + 13 \\right)} \\, dx", "reference_antiderivative": "4*x*log(4*x + 13) - 4*x + 13*log(4*x + 13)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0793", "stage": "atomic", "k": 1, "integrand": "log(15*x + 5)", "integrand_latex": "\\log{\\left(15 x + 5 \\right)}", "integrand_latex_integral": "\\int \\log{\\left(15 x + 5 \\right)} \\, dx", "reference_antiderivative": "x*log(15*x + 5) - x + log(3*x + 1)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0794", "stage": "atomic", "k": 1, "integrand": "-3/(-14*x - 12)", "integrand_latex": "- \\frac{3}{- 14 x - 12}", "integrand_latex_integral": "\\int - \\frac{3}{- 14 x - 12} \\, dx", "reference_antiderivative": "3*log(14*x + 12)/14", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0795", "stage": "atomic", "k": 1, "integrand": "log(7*x + 2)", "integrand_latex": "\\log{\\left(7 x + 2 \\right)}", "integrand_latex_integral": "\\int \\log{\\left(7 x + 2 \\right)} \\, dx", "reference_antiderivative": "x*log(7*x + 2) - x + 2*log(7*x + 2)/7", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0796", "stage": "atomic", "k": 1, "integrand": "5/(-6*x - 6)", "integrand_latex": "\\frac{5}{- 6 x - 6}", "integrand_latex_integral": "\\int \\frac{5}{- 6 x - 6} \\, dx", "reference_antiderivative": "-5*log(6*x + 6)/6", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0797", "stage": "atomic", "k": 1, "integrand": "log(3*x + 2)", "integrand_latex": "\\log{\\left(3 x + 2 \\right)}", "integrand_latex_integral": "\\int \\log{\\left(3 x + 2 \\right)} \\, dx", "reference_antiderivative": "x*log(3*x + 2) - x + 2*log(3*x + 2)/3", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0798", "stage": "atomic", "k": 1, "integrand": "-5*log(-4*x - 15)", "integrand_latex": "- 5 \\log{\\left(- 4 x - 15 \\right)}", "integrand_latex_integral": "\\int - 5 \\log{\\left(- 4 x - 15 \\right)} \\, dx", "reference_antiderivative": "-5*x*log(-4*x - 15) + 5*x - 75*log(4*x + 15)/4", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0799", "stage": "atomic", "k": 1, "integrand": "5/(5*x + 4)", "integrand_latex": "\\frac{5}{5 x + 4}", "integrand_latex_integral": "\\int \\frac{5}{5 x + 4} \\, dx", "reference_antiderivative": "log(5*x + 4)", "category": "logarithmic_rational", "variable": "x"}
{"id": "atom-0800", "stage": "atomic", "k": 1, "integrand": "4*x*sin(15*x + 9)", "integrand_latex": "4 x \\sin{\\left(15 x + 9 \\right)}", "integrand_latex_integral": "\\int 4 x \\sin{\\left(15 x + 9 \\right)} \\, dx", "reference_antiderivative": "-4*x*cos(15*x + 9)/15 + 4*sin(15*x + 9)/225", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0801", "stage": "atomic", "k": 1, "integrand": "-4*x*cos(12*x - 12)", "integrand_latex": "- 4 x \\cos{\\left(12 x - 12 \\right)}", "integrand_latex_integral": "\\int - 4 x \\cos{\\left(12 x - 12 \\right)} \\, dx", "reference_antiderivative": "-x*sin(12*x - 12)/3 - cos(12*x - 12)/36", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0802", "stage": "atomic", "k": 1, "integrand": "2*x*cos(13*x + 6)", "integrand_latex": "2 x \\cos{\\left(13 x + 6 \\right)}", "integrand_latex_integral": "\\int 2 x \\cos{\\left(13 x + 6 \\right)} \\, dx", "reference_antiderivative": "2*x*sin(13*x + 6)/13 + 2*cos(13*x + 6)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0803", "stage": "atomic", "k": 1, "integrand": "3*x*cos(3*x + 10)", "integrand_latex": "3 x \\cos{\\left(3 x + 10 \\right)}", "integrand_latex_integral": "\\int 3 x \\cos{\\left(3 x + 10 \\right)} \\, dx", "reference_antiderivative": "x*sin(3*x + 10) + cos(3*x + 10)/3", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0804", "stage": "atomic", "k": 1, "integrand": "-3*x*cos(x + 14)", "integrand_latex": "- 3 x \\cos{\\left(x + 14 \\right)}", "integrand_latex_integral": "\\int - 3 x \\cos{\\left(x + 14 \\right)} \\, dx", "reference_antiderivative": "-3*x*sin(x + 14) - 3*cos(x + 14)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0805", "stage": "atomic", "k": 1, "integrand": "-x*cos(8*x - 11)", "integrand_latex": "- x \\cos{\\left(8 x - 11 \\right)}", "integrand_latex_integral": "\\int - x \\cos{\\left(8 x - 11 \\right)} \\, dx", "reference_antiderivative": "-x*sin(8*x - 11)/8 - cos(8*x - 11)/64", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0806", "stage": "atomic", "k": 1, "integrand": "-3*x*exp(9*x + 7)", "integrand_latex": "- 3 x e^{9 x + 7}", "integrand_latex_integral": "\\int - 3 x e^{9 x + 7} \\, dx", "reference_antiderivative": "(1 - 9*x)*exp(9*x + 7)/27", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0807", "stage": "atomic", "k": 1, "integrand": "-3*x*atan(2*x - 9)", "integrand_latex": "- 3 x \\operatorname{atan}{\\left(2 x - 9 \\right)}", "integrand_latex_integral": "\\int - 3 x \\operatorname{atan}{\\left(2 x - 9 \\right)} \\, dx", "reference_antiderivative": "-3*x**2*atan(2*x - 9)/2 + 3*x/4 + 27*log(2*x**2 - 18*x + 41)/8 + 30*atan(2*x - 9)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0808", "stage": "atomic", "k": 1, "integrand": "-5*x*atan(11*x - 3)", "integrand_latex": "- 5 x \\operatorname{atan}{\\left(11 x - 3 \\right)}", "integrand_latex_integral": "\\int - 5 x \\operatorname{atan}{\\left(11 x - 3 \\right)} \\, dx", "reference_antiderivative": "-5*x**2*atan(11*x - 3)/2 + 5*x/22 + 15*log(121*x**2 - 66*x + 10)/242 + 20*atan(11*x - 3)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0809", "stage": "atomic", "k": 1, "integrand": "3*x*log(6*x + 12)", "integrand_latex": "3 x \\log{\\left(6 x + 12 \\right)}", "integrand_latex_integral": "\\int 3 x \\log{\\left(6 x + 12 \\right)} \\, dx", "reference_antiderivative": "3*x**2*log(6*x + 12)/2 - 3*x**2/4 + 3*x - 6*log(x + 2)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0810", "stage": "atomic", "k": 1, "integrand": "-2*x*log(-6*x - 13)", "integrand_latex": "- 2 x \\log{\\left(- 6 x - 13 \\right)}", "integrand_latex_integral": "\\int - 2 x \\log{\\left(- 6 x - 13 \\right)} \\, dx", "reference_antiderivative": "-x**2*log(-6*x - 13) + x**2/2 - 13*x/6 + 169*log(6*x + 13)/36", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0811", "stage": "atomic", "k": 1, "integrand": "-5*x*atan(x + 3)", "integrand_latex": "- 5 x \\operatorname{atan}{\\left(x + 3 \\right)}", "integrand_latex_integral": "\\int - 5 x \\operatorname{atan}{\\left(x + 3 \\right)} \\, dx", "reference_antiderivative": "-5*x**2*atan(x + 3)/2 + 5*x/2 - 15*log(x**2 + 6*x + 10)/2 + 20*atan(x + 3)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0812", "stage": "atomic", "k": 1, "integrand": "5*x*exp(4*x - 11)", "integrand_latex": "5 x e^{4 x - 11}", "integrand_latex_integral": "\\int 5 x e^{4 x - 11} \\, dx", "reference_antiderivative": "(20*x - 5)*exp(4*x - 11)/16", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0813", "stage": "atomic", "k": 1, "integrand": "-2*x*sin(10*x - 15)", "integrand_latex": "- 2 x \\sin{\\left(10 x - 15 \\right)}", "integrand_latex_integral": "\\int - 2 x \\sin{\\left(10 x - 15 \\right)} \\, dx", "reference_antiderivative": "x*cos(10*x - 15)/5 - sin(10*x - 15)/50", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0814", "stage": "atomic", "k": 1, "integrand": "-2*x*log(-11*x - 14)", "integrand_latex": "- 2 x \\log{\\left(- 11 x - 14 \\right)}", "integrand_latex_integral": "\\int - 2 x \\log{\\left(- 11 x - 14 \\right)} \\, dx", "reference_antiderivative": "-x**2*log(-11*x - 14) + x**2/2 - 14*x/11 + 196*log(11*x + 14)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0815", "stage": "atomic", "k": 1, "integrand": "-5*x*sin(2*x + 9)", "integrand_latex": "- 5 x \\sin{\\left(2 x + 9 \\right)}", "integrand_latex_integral": "\\int - 5 x \\sin{\\left(2 x + 9 \\right)} \\, dx", "reference_antiderivative": "5*x*cos(2*x + 9)/2 - 5*sin(2*x + 9)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0816", "stage": "atomic", "k": 1, "integrand": "-x*exp(14 - 5*x)", "integrand_latex": "- x e^{14 - 5 x}", "integrand_latex_integral": "\\int - x e^{14 - 5 x} \\, dx", "reference_antiderivative": "(5*x + 1)*exp(14 - 5*x)/25", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0817", "stage": "atomic", "k": 1, "integrand": "3*x*cos(3*x - 2)", "integrand_latex": "3 x \\cos{\\left(3 x - 2 \\right)}", "integrand_latex_integral": "\\int 3 x \\cos{\\left(3 x - 2 \\right)} \\, dx", "reference_antiderivative": "x*sin(3*x - 2) + cos(3*x - 2)/3", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0818", "stage": "atomic", "k": 1, "integrand": "3*x*exp(14 - x)", "integrand_latex": "3 x e^{14 - x}", "integrand_latex_integral": "\\int 3 x e^{14 - x} \\, dx", "reference_antiderivative": "(-3*x - 3)*exp(14 - x)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0819", "stage": "atomic", "k": 1, "integrand": "4*x*log(3*x + 1)", "integrand_latex": "4 x \\log{\\left(3 x + 1 \\right)}", "integrand_latex_integral": "\\int 4 x \\log{\\left(3 x + 1 \\right)} \\, dx", "reference_antiderivative": "2*x**2*log(3*x + 1) - x**2 + 2*x/3 - 2*log(3*x + 1)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0820", "stage": "atomic", "k": 1, "integrand": "3*x*atan(11*x - 3)", "integrand_latex": "3 x \\operatorname{atan}{\\left(11 x - 3 \\right)}", "integrand_latex_integral": "\\int 3 x \\operatorname{atan}{\\left(11 x - 3 \\right)} \\, dx", "reference_antiderivative": "3*x**2*atan(11*x - 3)/2 - 3*x/22 - 9*log(121*x**2 - 66*x + 10)/242 - 12*atan(11*x - 3)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0821", "stage": "atomic", "k": 1, "integrand": "-4*x*atan(14*x - 12)", "integrand_latex": "- 4 x \\operatorname{atan}{\\left(14 x - 12 \\right)}", "integrand_latex_integral": "\\int - 4 x \\operatorname{atan}{\\left(14 x - 12 \\right)} \\, dx", "reference_antiderivative": "-2*x**2*atan(14*x - 12) + x/7 + 6*log(196*x**2 - 336*x + 145)/49 + 143*atan(14*x - 12)/98", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0822", "stage": "atomic", "k": 1, "integrand": "-x*cos(12*x + 2)", "integrand_latex": "- x \\cos{\\left(12 x + 2 \\right)}", "integrand_latex_integral": "\\int - x \\cos{\\left(12 x + 2 \\right)} \\, dx", "reference_antiderivative": "-x*sin(12*x + 2)/12 - cos(12*x + 2)/144", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0823", "stage": "atomic", "k": 1, "integrand": "-x*log(5 - 3*x)", "integrand_latex": "- x \\log{\\left(5 - 3 x \\right)}", "integrand_latex_integral": "\\int - x \\log{\\left(5 - 3 x \\right)} \\, dx", "reference_antiderivative": "-x**2*log(5 - 3*x)/2 + x**2/4 + 5*x/6 + 25*log(3*x - 5)/18", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0824", "stage": "atomic", "k": 1, "integrand": "2*x*cos(14*x + 10)", "integrand_latex": "2 x \\cos{\\left(14 x + 10 \\right)}", "integrand_latex_integral": "\\int 2 x \\cos{\\left(14 x + 10 \\right)} \\, dx", "reference_antiderivative": "x*sin(14*x + 10)/7 + cos(14*x + 10)/98", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0825", "stage": "atomic", "k": 1, "integrand": "4*x*log(4*x + 6)", "integrand_latex": "4 x \\log{\\left(4 x + 6 \\right)}", "integrand_latex_integral": "\\int 4 x \\log{\\left(4 x + 6 \\right)} \\, dx", "reference_antiderivative": "2*x**2*log(4*x + 6) - x**2 + 3*x - 9*log(2*x + 3)/2", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0826", "stage": "atomic", "k": 1, "integrand": "-2*x*log(8 - 14*x)", "integrand_latex": "- 2 x \\log{\\left(8 - 14 x \\right)}", "integrand_latex_integral": "\\int - 2 x \\log{\\left(8 - 14 x \\right)} \\, dx", "reference_antiderivative": "-x**2*log(8 - 14*x) + x**2/2 + 4*x/7 + 16*log(7*x - 4)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0827", "stage": "atomic", "k": 1, "integrand": "-5*x*cos(5*x - 11)", "integrand_latex": "- 5 x \\cos{\\left(5 x - 11 \\right)}", "integrand_latex_integral": "\\int - 5 x \\cos{\\left(5 x - 11 \\right)} \\, dx", "reference_antiderivative": "-x*sin(5*x - 11) - cos(5*x - 11)/5", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0828", "stage": "atomic", "k": 1, "integrand": "2*x*exp(12*x + 7)", "integrand_latex": "2 x e^{12 x + 7}", "integrand_latex_integral": "\\int 2 x e^{12 x + 7} \\, dx", "reference_antiderivative": "(12*x - 1)*exp(12*x + 7)/72", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0829", "stage": "atomic", "k": 1, "integrand": "-2*x*log(-11*x - 6)", "integrand_latex": "- 2 x \\log{\\left(- 11 x - 6 \\right)}", "integrand_latex_integral": "\\int - 2 x \\log{\\left(- 11 x - 6 \\right)} \\, dx", "reference_antiderivative": "-x**2*log(-11*x - 6) + x**2/2 - 6*x/11 + 36*log(11*x + 6)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0830", "stage": "atomic", "k": 1, "integrand": "-x*atan(8*x - 2)", "integrand_latex": "- x \\operatorname{atan}{\\left(8 x - 2 \\right)}", "integrand_latex_integral": "\\int - x \\operatorname{atan}{\\left(8 x - 2 \\right)} \\, dx", "reference_antiderivative": "-x**2*atan(8*x - 2)/2 + x/16 + log(64*x**2 - 32*x + 5)/64 + 3*atan(8*x - 2)/128", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0831", "stage": "atomic", "k": 1, "integrand": "-2*x*log(-x - 9)", "integrand_latex": "- 2 x \\log{\\left(- x - 9 \\right)}", "integrand_latex_integral": "\\int - 2 x \\log{\\left(- x - 9 \\right)} \\, dx", "reference_antiderivative": "-x**2*log(-x - 9) + x**2/2 - 9*x + 81*log(x + 9)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0832", "stage": "atomic", "k": 1, "integrand": "3*x*exp(12*x - 4)", "integrand_latex": "3 x e^{12 x - 4}", "integrand_latex_integral": "\\int 3 x e^{12 x - 4} \\, dx", "reference_antiderivative": "(12*x - 1)*exp(12*x - 4)/48", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0833", "stage": "atomic", "k": 1, "integrand": "3*x*atan(13*x + 6)", "integrand_latex": "3 x \\operatorname{atan}{\\left(13 x + 6 \\right)}", "integrand_latex_integral": "\\int 3 x \\operatorname{atan}{\\left(13 x + 6 \\right)} \\, dx", "reference_antiderivative": "3*x**2*atan(13*x + 6)/2 - 3*x/26 + 9*log(169*x**2 + 156*x + 37)/169 - 105*atan(13*x + 6)/338", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0834", "stage": "atomic", "k": 1, "integrand": "3*x*exp(13*x + 3)", "integrand_latex": "3 x e^{13 x + 3}", "integrand_latex_integral": "\\int 3 x e^{13 x + 3} \\, dx", "reference_antiderivative": "(39*x - 3)*exp(13*x + 3)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0835", "stage": "atomic", "k": 1, "integrand": "-2*x*sin(11*x - 14)", "integrand_latex": "- 2 x \\sin{\\left(11 x - 14 \\right)}", "integrand_latex_integral": "\\int - 2 x \\sin{\\left(11 x - 14 \\right)} \\, dx", "reference_antiderivative": "2*x*cos(11*x - 14)/11 - 2*sin(11*x - 14)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0836", "stage": "atomic", "k": 1, "integrand": "-5*x*sin(14*x - 4)", "integrand_latex": "- 5 x \\sin{\\left(14 x - 4 \\right)}", "integrand_latex_integral": "\\int - 5 x \\sin{\\left(14 x - 4 \\right)} \\, dx", "reference_antiderivative": "5*x*cos(14*x - 4)/14 - 5*sin(14*x - 4)/196", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0837", "stage": "atomic", "k": 1, "integrand": "2*x*exp(x - 3)", "integrand_latex": "2 x e^{x - 3}", "integrand_latex_integral": "\\int 2 x e^{x - 3} \\, dx", "reference_antiderivative": "(2*x - 2)*exp(x - 3)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0838", "stage": "atomic", "k": 1, "integrand": "2*x*atan(4*x)", "integrand_latex": "2 x \\operatorname{atan}{\\left(4 x \\right)}", "integrand_latex_integral": "\\int 2 x \\operatorname{atan}{\\left(4 x \\right)} \\, dx", "reference_antiderivative": "x**2*atan(4*x) - x/4 + atan(4*x)/16", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0839", "stage": "atomic", "k": 1, "integrand": "2*x*cos(3*x + 2)", "integrand_latex": "2 x \\cos{\\left(3 x + 2 \\right)}", "integrand_latex_integral": "\\int 2 x \\cos{\\left(3 x + 2 \\right)} \\, dx", "reference_antiderivative": "2*x*sin(3*x + 2)/3 + 2*cos(3*x + 2)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0840", "stage": "atomic", "k": 1, "integrand": "-x*exp(8*x + 11)", "integrand_latex": "- x e^{8 x + 11}", "integrand_latex_integral": "\\int - x e^{8 x + 11} \\, dx", "reference_antiderivative": "(1 - 8*x)*exp(8*x + 11)/64", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0841", "stage": "atomic", "k": 1, "integrand": "-x*atan(14*x + 10)", "integrand_latex": "- x \\operatorname{atan}{\\left(14 x + 10 \\right)}", "integrand_latex_integral": "\\int - x \\operatorname{atan}{\\left(14 x + 10 \\right)} \\, dx", "reference_antiderivative": "-x**2*atan(14*x + 10)/2 + x/28 - 5*log(196*x**2 + 280*x + 101)/196 + 99*atan(14*x + 10)/392", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0842", "stage": "atomic", "k": 1, "integrand": "-2*x*sin(12*x - 8)", "integrand_latex": "- 2 x \\sin{\\left(12 x - 8 \\right)}", "integrand_latex_integral": "\\int - 2 x \\sin{\\left(12 x - 8 \\right)} \\, dx", "reference_antiderivative": "x*cos(12*x - 8)/6 - sin(12*x - 8)/72", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0843", "stage": "atomic", "k": 1, "integrand": "-x*atan(5*x - 2)", "integrand_latex": "- x \\operatorname{atan}{\\left(5 x - 2 \\right)}", "integrand_latex_integral": "\\int - x \\operatorname{atan}{\\left(5 x - 2 \\right)} \\, dx", "reference_antiderivative": "-x**2*atan(5*x - 2)/2 + x/10 + log(5*x**2 - 4*x + 1)/25 + 3*atan(5*x - 2)/50", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0844", "stage": "atomic", "k": 1, "integrand": "-5*x*sin(15*x)", "integrand_latex": "- 5 x \\sin{\\left(15 x \\right)}", "integrand_latex_integral": "\\int - 5 x \\sin{\\left(15 x \\right)} \\, dx", "reference_antiderivative": "x*cos(15*x)/3 - sin(15*x)/45", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0845", "stage": "atomic", "k": 1, "integrand": "4*x*sin(10*x - 15)", "integrand_latex": "4 x \\sin{\\left(10 x - 15 \\right)}", "integrand_latex_integral": "\\int 4 x \\sin{\\left(10 x - 15 \\right)} \\, dx", "reference_antiderivative": "-2*x*cos(10*x - 15)/5 + sin(10*x - 15)/25", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0846", "stage": "atomic", "k": 1, "integrand": "-x*cos(7*x + 15)", "integrand_latex": "- x \\cos{\\left(7 x + 15 \\right)}", "integrand_latex_integral": "\\int - x \\cos{\\left(7 x + 15 \\right)} \\, dx", "reference_antiderivative": "-x*sin(7*x + 15)/7 - cos(7*x + 15)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0847", "stage": "atomic", "k": 1, "integrand": "x*log(12*x - 4)", "integrand_latex": "x \\log{\\left(12 x - 4 \\right)}", "integrand_latex_integral": "\\int x \\log{\\left(12 x - 4 \\right)} \\, dx", "reference_antiderivative": "x**2*log(12*x - 4)/2 - x**2/4 - x/6 - log(3*x - 1)/18", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0848", "stage": "atomic", "k": 1, "integrand": "-2*x*atan(6*x - 6)", "integrand_latex": "- 2 x \\operatorname{atan}{\\left(6 x - 6 \\right)}", "integrand_latex_integral": "\\int - 2 x \\operatorname{atan}{\\left(6 x - 6 \\right)} \\, dx", "reference_antiderivative": "-x**2*atan(6*x - 6) + x/6 + log(36*x**2 - 72*x + 37)/6 + 35*atan(6*x - 6)/36", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0849", "stage": "atomic", "k": 1, "integrand": "x*exp(3*x - 12)", "integrand_latex": "x e^{3 x - 12}", "integrand_latex_integral": "\\int x e^{3 x - 12} \\, dx", "reference_antiderivative": "(3*x - 1)*exp(3*x - 12)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0850", "stage": "atomic", "k": 1, "integrand": "5*x*cos(15*x + 11)", "integrand_latex": "5 x \\cos{\\left(15 x + 11 \\right)}", "integrand_latex_integral": "\\int 5 x \\cos{\\left(15 x + 11 \\right)} \\, dx", "reference_antiderivative": "x*sin(15*x + 11)/3 + cos(15*x + 11)/45", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0851", "stage": "atomic", "k": 1, "integrand": "4*x*cos(4*x - 6)", "integrand_latex": "4 x \\cos{\\left(4 x - 6 \\right)}", "integrand_latex_integral": "\\int 4 x \\cos{\\left(4 x - 6 \\right)} \\, dx", "reference_antiderivative": "x*sin(4*x - 6) + cos(4*x - 6)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0852", "stage": "atomic", "k": 1, "integrand": "2*x*cos(13*x + 5)", "integrand_latex": "2 x \\cos{\\left(13 x + 5 \\right)}", "integrand_latex_integral": "\\int 2 x \\cos{\\left(13 x + 5 \\right)} \\, dx", "reference_antiderivative": "2*x*sin(13*x + 5)/13 + 2*cos(13*x + 5)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0853", "stage": "atomic", "k": 1, "integrand": "-x*cos(7*x - 5)", "integrand_latex": "- x \\cos{\\left(7 x - 5 \\right)}", "integrand_latex_integral": "\\int - x \\cos{\\left(7 x - 5 \\right)} \\, dx", "reference_antiderivative": "-x*sin(7*x - 5)/7 - cos(7*x - 5)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0854", "stage": "atomic", "k": 1, "integrand": "3*x*exp(9*x - 8)", "integrand_latex": "3 x e^{9 x - 8}", "integrand_latex_integral": "\\int 3 x e^{9 x - 8} \\, dx", "reference_antiderivative": "(9*x - 1)*exp(9*x - 8)/27", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0855", "stage": "atomic", "k": 1, "integrand": "4*x*cos(3*x - 6)", "integrand_latex": "4 x \\cos{\\left(3 x - 6 \\right)}", "integrand_latex_integral": "\\int 4 x \\cos{\\left(3 x - 6 \\right)} \\, dx", "reference_antiderivative": "4*x*sin(3*x - 6)/3 + 4*cos(3*x - 6)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0856", "stage": "atomic", "k": 1, "integrand": "-5*x*cos(5*x)", "integrand_latex": "- 5 x \\cos{\\left(5 x \\right)}", "integrand_latex_integral": "\\int - 5 x \\cos{\\left(5 x \\right)} \\, dx", "reference_antiderivative": "-x*sin(5*x) - cos(5*x)/5", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0857", "stage": "atomic", "k": 1, "integrand": "x*exp(-3*x - 3)", "integrand_latex": "x e^{- 3 x - 3}", "integrand_latex_integral": "\\int x e^{- 3 x - 3} \\, dx", "reference_antiderivative": "(-3*x - 1)*exp(-3*x - 3)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0858", "stage": "atomic", "k": 1, "integrand": "4*x*cos(11*x - 9)", "integrand_latex": "4 x \\cos{\\left(11 x - 9 \\right)}", "integrand_latex_integral": "\\int 4 x \\cos{\\left(11 x - 9 \\right)} \\, dx", "reference_antiderivative": "4*x*sin(11*x - 9)/11 + 4*cos(11*x - 9)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0859", "stage": "atomic", "k": 1, "integrand": "-2*x*log(6*x + 2)", "integrand_latex": "- 2 x \\log{\\left(6 x + 2 \\right)}", "integrand_latex_integral": "\\int - 2 x \\log{\\left(6 x + 2 \\right)} \\, dx", "reference_antiderivative": "-x**2*log(6*x + 2) + x**2/2 - x/3 + log(3*x + 1)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0860", "stage": "atomic", "k": 1, "integrand": "5*x*cos(4*x - 1)", "integrand_latex": "5 x \\cos{\\left(4 x - 1 \\right)}", "integrand_latex_integral": "\\int 5 x \\cos{\\left(4 x - 1 \\right)} \\, dx", "reference_antiderivative": "5*x*sin(4*x - 1)/4 + 5*cos(4*x - 1)/16", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0861", "stage": "atomic", "k": 1, "integrand": "5*x*sin(13*x + 2)", "integrand_latex": "5 x \\sin{\\left(13 x + 2 \\right)}", "integrand_latex_integral": "\\int 5 x \\sin{\\left(13 x + 2 \\right)} \\, dx", "reference_antiderivative": "-5*x*cos(13*x + 2)/13 + 5*sin(13*x + 2)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0862", "stage": "atomic", "k": 1, "integrand": "2*x*cos(11*x - 8)", "integrand_latex": "2 x \\cos{\\left(11 x - 8 \\right)}", "integrand_latex_integral": "\\int 2 x \\cos{\\left(11 x - 8 \\right)} \\, dx", "reference_antiderivative": "2*x*sin(11*x - 8)/11 + 2*cos(11*x - 8)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0863", "stage": "atomic", "k": 1, "integrand": "3*x*sin(9*x + 14)", "integrand_latex": "3 x \\sin{\\left(9 x + 14 \\right)}", "integrand_latex_integral": "\\int 3 x \\sin{\\left(9 x + 14 \\right)} \\, dx", "reference_antiderivative": "-x*cos(9*x + 14)/3 + sin(9*x + 14)/27", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0864", "stage": "atomic", "k": 1, "integrand": "5*x*cos(13*x + 8)", "integrand_latex": "5 x \\cos{\\left(13 x + 8 \\right)}", "integrand_latex_integral": "\\int 5 x \\cos{\\left(13 x + 8 \\right)} \\, dx", "reference_antiderivative": "5*x*sin(13*x + 8)/13 + 5*cos(13*x + 8)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0865", "stage": "atomic", "k": 1, "integrand": "-x*cos(2*x - 10)", "integrand_latex": "- x \\cos{\\left(2 x - 10 \\right)}", "integrand_latex_integral": "\\int - x \\cos{\\left(2 x - 10 \\right)} \\, dx", "reference_antiderivative": "-x*sin(2*x - 10)/2 - cos(2*x - 10)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0866", "stage": "atomic", "k": 1, "integrand": "4*x*exp(-6*x - 1)", "integrand_latex": "4 x e^{- 6 x - 1}", "integrand_latex_integral": "\\int 4 x e^{- 6 x - 1} \\, dx", "reference_antiderivative": "(-6*x - 1)*exp(-6*x - 1)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0867", "stage": "atomic", "k": 1, "integrand": "5*x*atan(3*x + 3)", "integrand_latex": "5 x \\operatorname{atan}{\\left(3 x + 3 \\right)}", "integrand_latex_integral": "\\int 5 x \\operatorname{atan}{\\left(3 x + 3 \\right)} \\, dx", "reference_antiderivative": "5*x**2*atan(3*x + 3)/2 - 5*x/6 + 5*log(9*x**2 + 18*x + 10)/6 - 20*atan(3*x + 3)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0868", "stage": "atomic", "k": 1, "integrand": "-2*x*log(x - 12)", "integrand_latex": "- 2 x \\log{\\left(x - 12 \\right)}", "integrand_latex_integral": "\\int - 2 x \\log{\\left(x - 12 \\right)} \\, dx", "reference_antiderivative": "-x**2*log(x - 12) + x**2/2 + 12*x + 144*log(x - 12)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0869", "stage": "atomic", "k": 1, "integrand": "-x*sin(14*x - 12)", "integrand_latex": "- x \\sin{\\left(14 x - 12 \\right)}", "integrand_latex_integral": "\\int - x \\sin{\\left(14 x - 12 \\right)} \\, dx", "reference_antiderivative": "x*cos(14*x - 12)/14 - sin(14*x - 12)/196", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0870", "stage": "atomic", "k": 1, "integrand": "2*x*atan(5*x + 2)", "integrand_latex": "2 x \\operatorname{atan}{\\left(5 x + 2 \\right)}", "integrand_latex_integral": "\\int 2 x \\operatorname{atan}{\\left(5 x + 2 \\right)} \\, dx", "reference_antiderivative": "x**2*atan(5*x + 2) - x/5 + 2*log(5*x**2 + 4*x + 1)/25 - 3*atan(5*x + 2)/25", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0871", "stage": "atomic", "k": 1, "integrand": "-2*x*sin(11*x + 5)", "integrand_latex": "- 2 x \\sin{\\left(11 x + 5 \\right)}", "integrand_latex_integral": "\\int - 2 x \\sin{\\left(11 x + 5 \\right)} \\, dx", "reference_antiderivative": "2*x*cos(11*x + 5)/11 - 2*sin(11*x + 5)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0872", "stage": "atomic", "k": 1, "integrand": "-2*x*sin(5*x - 5)", "integrand_latex": "- 2 x \\sin{\\left(5 x - 5 \\right)}", "integrand_latex_integral": "\\int - 2 x \\sin{\\left(5 x - 5 \\right)} \\, dx", "reference_antiderivative": "2*x*cos(5*x - 5)/5 - 2*sin(5*x - 5)/25", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0873", "stage": "atomic", "k": 1, "integrand": "-5*x*cos(15*x + 1)", "integrand_latex": "- 5 x \\cos{\\left(15 x + 1 \\right)}", "integrand_latex_integral": "\\int - 5 x \\cos{\\left(15 x + 1 \\right)} \\, dx", "reference_antiderivative": "-x*sin(15*x + 1)/3 - cos(15*x + 1)/45", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0874", "stage": "atomic", "k": 1, "integrand": "-3*x*sin(3*x + 9)", "integrand_latex": "- 3 x \\sin{\\left(3 x + 9 \\right)}", "integrand_latex_integral": "\\int - 3 x \\sin{\\left(3 x + 9 \\right)} \\, dx", "reference_antiderivative": "x*cos(3*x + 9) - sin(3*x + 9)/3", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0875", "stage": "atomic", "k": 1, "integrand": "-4*x*log(4 - 11*x)", "integrand_latex": "- 4 x \\log{\\left(4 - 11 x \\right)}", "integrand_latex_integral": "\\int - 4 x \\log{\\left(4 - 11 x \\right)} \\, dx", "reference_antiderivative": "-2*x**2*log(4 - 11*x) + x**2 + 8*x/11 + 32*log(11*x - 4)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0876", "stage": "atomic", "k": 1, "integrand": "x*log(15 - 2*x)", "integrand_latex": "x \\log{\\left(15 - 2 x \\right)}", "integrand_latex_integral": "\\int x \\log{\\left(15 - 2 x \\right)} \\, dx", "reference_antiderivative": "x**2*log(15 - 2*x)/2 - x**2/4 - 15*x/4 - 225*log(2*x - 15)/8", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0877", "stage": "atomic", "k": 1, "integrand": "-5*x*cos(2*x - 9)", "integrand_latex": "- 5 x \\cos{\\left(2 x - 9 \\right)}", "integrand_latex_integral": "\\int - 5 x \\cos{\\left(2 x - 9 \\right)} \\, dx", "reference_antiderivative": "-5*x*sin(2*x - 9)/2 - 5*cos(2*x - 9)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0878", "stage": "atomic", "k": 1, "integrand": "3*x*exp(-9*x - 15)", "integrand_latex": "3 x e^{- 9 x - 15}", "integrand_latex_integral": "\\int 3 x e^{- 9 x - 15} \\, dx", "reference_antiderivative": "(-9*x - 1)*exp(-9*x - 15)/27", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0879", "stage": "atomic", "k": 1, "integrand": "-2*x*cos(8*x - 7)", "integrand_latex": "- 2 x \\cos{\\left(8 x - 7 \\right)}", "integrand_latex_integral": "\\int - 2 x \\cos{\\left(8 x - 7 \\right)} \\, dx", "reference_antiderivative": "-x*sin(8*x - 7)/4 - cos(8*x - 7)/32", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0880", "stage": "atomic", "k": 1, "integrand": "4*x*atan(3*x - 1)", "integrand_latex": "4 x \\operatorname{atan}{\\left(3 x - 1 \\right)}", "integrand_latex_integral": "\\int 4 x \\operatorname{atan}{\\left(3 x - 1 \\right)} \\, dx", "reference_antiderivative": "2*x**2*atan(3*x - 1) - 2*x/3 - 2*log(9*x**2 - 6*x + 2)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0881", "stage": "atomic", "k": 1, "integrand": "-4*x*cos(11*x - 14)", "integrand_latex": "- 4 x \\cos{\\left(11 x - 14 \\right)}", "integrand_latex_integral": "\\int - 4 x \\cos{\\left(11 x - 14 \\right)} \\, dx", "reference_antiderivative": "-4*x*sin(11*x - 14)/11 - 4*cos(11*x - 14)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0882", "stage": "atomic", "k": 1, "integrand": "2*x*atan(8*x + 1)", "integrand_latex": "2 x \\operatorname{atan}{\\left(8 x + 1 \\right)}", "integrand_latex_integral": "\\int 2 x \\operatorname{atan}{\\left(8 x + 1 \\right)} \\, dx", "reference_antiderivative": "x**2*atan(8*x + 1) - x/8 + log(32*x**2 + 8*x + 1)/64", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0883", "stage": "atomic", "k": 1, "integrand": "x*sin(13*x + 6)", "integrand_latex": "x \\sin{\\left(13 x + 6 \\right)}", "integrand_latex_integral": "\\int x \\sin{\\left(13 x + 6 \\right)} \\, dx", "reference_antiderivative": "-x*cos(13*x + 6)/13 + sin(13*x + 6)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0884", "stage": "atomic", "k": 1, "integrand": "-2*x*sin(4*x - 9)", "integrand_latex": "- 2 x \\sin{\\left(4 x - 9 \\right)}", "integrand_latex_integral": "\\int - 2 x \\sin{\\left(4 x - 9 \\right)} \\, dx", "reference_antiderivative": "x*cos(4*x - 9)/2 - sin(4*x - 9)/8", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0885", "stage": "atomic", "k": 1, "integrand": "-x*sin(15*x + 8)", "integrand_latex": "- x \\sin{\\left(15 x + 8 \\right)}", "integrand_latex_integral": "\\int - x \\sin{\\left(15 x + 8 \\right)} \\, dx", "reference_antiderivative": "x*cos(15*x + 8)/15 - sin(15*x + 8)/225", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0886", "stage": "atomic", "k": 1, "integrand": "-3*x*exp(8 - 9*x)", "integrand_latex": "- 3 x e^{8 - 9 x}", "integrand_latex_integral": "\\int - 3 x e^{8 - 9 x} \\, dx", "reference_antiderivative": "(9*x + 1)*exp(8 - 9*x)/27", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0887", "stage": "atomic", "k": 1, "integrand": "-3*x*exp(-12*x - 4)", "integrand_latex": "- 3 x e^{- 12 x - 4}", "integrand_latex_integral": "\\int - 3 x e^{- 12 x - 4} \\, dx", "reference_antiderivative": "(12*x + 1)*exp(-12*x - 4)/48", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0888", "stage": "atomic", "k": 1, "integrand": "-5*x*atan(7*x - 9)", "integrand_latex": "- 5 x \\operatorname{atan}{\\left(7 x - 9 \\right)}", "integrand_latex_integral": "\\int - 5 x \\operatorname{atan}{\\left(7 x - 9 \\right)} \\, dx", "reference_antiderivative": "-5*x**2*atan(7*x - 9)/2 + 5*x/14 + 45*log(49*x**2 - 126*x + 82)/98 + 200*atan(7*x - 9)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0889", "stage": "atomic", "k": 1, "integrand": "4*x*exp(6 - 14*x)", "integrand_latex": "4 x e^{6 - 14 x}", "integrand_latex_integral": "\\int 4 x e^{6 - 14 x} \\, dx", "reference_antiderivative": "(-14*x - 1)*exp(6 - 14*x)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0890", "stage": "atomic", "k": 1, "integrand": "-5*x*exp(7 - 14*x)", "integrand_latex": "- 5 x e^{7 - 14 x}", "integrand_latex_integral": "\\int - 5 x e^{7 - 14 x} \\, dx", "reference_antiderivative": "(70*x + 5)*exp(7 - 14*x)/196", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0891", "stage": "atomic", "k": 1, "integrand": "x*cos(12*x - 2)", "integrand_latex": "x \\cos{\\left(12 x - 2 \\right)}", "integrand_latex_integral": "\\int x \\cos{\\left(12 x - 2 \\right)} \\, dx", "reference_antiderivative": "x*sin(12*x - 2)/12 + cos(12*x - 2)/144", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0892", "stage": "atomic", "k": 1, "integrand": "-3*x*exp(7 - 9*x)", "integrand_latex": "- 3 x e^{7 - 9 x}", "integrand_latex_integral": "\\int - 3 x e^{7 - 9 x} \\, dx", "reference_antiderivative": "(9*x + 1)*exp(7 - 9*x)/27", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0893", "stage": "atomic", "k": 1, "integrand": "-5*x*atan(12*x - 6)", "integrand_latex": "- 5 x \\operatorname{atan}{\\left(12 x - 6 \\right)}", "integrand_latex_integral": "\\int - 5 x \\operatorname{atan}{\\left(12 x - 6 \\right)} \\, dx", "reference_antiderivative": "-5*x**2*atan(12*x - 6)/2 + 5*x/24 + 5*log(144*x**2 - 144*x + 37)/48 + 175*atan(12*x - 6)/288", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0894", "stage": "atomic", "k": 1, "integrand": "4*x*log(7*x - 11)", "integrand_latex": "4 x \\log{\\left(7 x - 11 \\right)}", "integrand_latex_integral": "\\int 4 x \\log{\\left(7 x - 11 \\right)} \\, dx", "reference_antiderivative": "2*x**2*log(7*x - 11) - x**2 - 22*x/7 - 242*log(7*x - 11)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0895", "stage": "atomic", "k": 1, "integrand": "-4*x*atan(x + 8)", "integrand_latex": "- 4 x \\operatorname{atan}{\\left(x + 8 \\right)}", "integrand_latex_integral": "\\int - 4 x \\operatorname{atan}{\\left(x + 8 \\right)} \\, dx", "reference_antiderivative": "-2*x**2*atan(x + 8) + 2*x - 16*log(x**2 + 16*x + 65) + 126*atan(x + 8)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0896", "stage": "atomic", "k": 1, "integrand": "-4*x*log(10*x - 12)", "integrand_latex": "- 4 x \\log{\\left(10 x - 12 \\right)}", "integrand_latex_integral": "\\int - 4 x \\log{\\left(10 x - 12 \\right)} \\, dx", "reference_antiderivative": "-2*x**2*log(10*x - 12) + x**2 + 12*x/5 + 72*log(5*x - 6)/25", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0897", "stage": "atomic", "k": 1, "integrand": "-2*x*atan(9*x - 7)", "integrand_latex": "- 2 x \\operatorname{atan}{\\left(9 x - 7 \\right)}", "integrand_latex_integral": "\\int - 2 x \\operatorname{atan}{\\left(9 x - 7 \\right)} \\, dx", "reference_antiderivative": "-x**2*atan(9*x - 7) + x/9 + 7*log(81*x**2 - 126*x + 50)/81 + 16*atan(9*x - 7)/27", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0898", "stage": "atomic", "k": 1, "integrand": "x*exp(-6*x - 10)", "integrand_latex": "x e^{- 6 x - 10}", "integrand_latex_integral": "\\int x e^{- 6 x - 10} \\, dx", "reference_antiderivative": "(-6*x - 1)*exp(-6*x - 10)/36", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0899", "stage": "atomic", "k": 1, "integrand": "-2*x*log(7*x + 14)", "integrand_latex": "- 2 x \\log{\\left(7 x + 14 \\right)}", "integrand_latex_integral": "\\int - 2 x \\log{\\left(7 x + 14 \\right)} \\, dx", "reference_antiderivative": "-x**2*log(7*x + 14) + x**2/2 - 2*x + 4*log(x + 2)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0900", "stage": "atomic", "k": 1, "integrand": "-5*x*exp(6 - 15*x)", "integrand_latex": "- 5 x e^{6 - 15 x}", "integrand_latex_integral": "\\int - 5 x e^{6 - 15 x} \\, dx", "reference_antiderivative": "(15*x + 1)*exp(6 - 15*x)/45", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0901", "stage": "atomic", "k": 1, "integrand": "4*x*sin(6*x)", "integrand_latex": "4 x \\sin{\\left(6 x \\right)}", "integrand_latex_integral": "\\int 4 x \\sin{\\left(6 x \\right)} \\, dx", "reference_antiderivative": "-2*x*cos(6*x)/3 + sin(6*x)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0902", "stage": "atomic", "k": 1, "integrand": "3*x*exp(8 - 13*x)", "integrand_latex": "3 x e^{8 - 13 x}", "integrand_latex_integral": "\\int 3 x e^{8 - 13 x} \\, dx", "reference_antiderivative": "(-39*x - 3)*exp(8 - 13*x)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0903", "stage": "atomic", "k": 1, "integrand": "5*x*cos(8*x + 1)", "integrand_latex": "5 x \\cos{\\left(8 x + 1 \\right)}", "integrand_latex_integral": "\\int 5 x \\cos{\\left(8 x + 1 \\right)} \\, dx", "reference_antiderivative": "5*x*sin(8*x + 1)/8 + 5*cos(8*x + 1)/64", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0904", "stage": "atomic", "k": 1, "integrand": "5*x*sin(12*x - 11)", "integrand_latex": "5 x \\sin{\\left(12 x - 11 \\right)}", "integrand_latex_integral": "\\int 5 x \\sin{\\left(12 x - 11 \\right)} \\, dx", "reference_antiderivative": "-5*x*cos(12*x - 11)/12 + 5*sin(12*x - 11)/144", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0905", "stage": "atomic", "k": 1, "integrand": "-x*cos(4*x - 10)", "integrand_latex": "- x \\cos{\\left(4 x - 10 \\right)}", "integrand_latex_integral": "\\int - x \\cos{\\left(4 x - 10 \\right)} \\, dx", "reference_antiderivative": "-x*sin(4*x - 10)/4 - cos(4*x - 10)/16", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0906", "stage": "atomic", "k": 1, "integrand": "-4*x*exp(12 - 12*x)", "integrand_latex": "- 4 x e^{12 - 12 x}", "integrand_latex_integral": "\\int - 4 x e^{12 - 12 x} \\, dx", "reference_antiderivative": "(12*x + 1)*exp(12 - 12*x)/36", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0907", "stage": "atomic", "k": 1, "integrand": "-3*x*sin(6*x + 5)", "integrand_latex": "- 3 x \\sin{\\left(6 x + 5 \\right)}", "integrand_latex_integral": "\\int - 3 x \\sin{\\left(6 x + 5 \\right)} \\, dx", "reference_antiderivative": "x*cos(6*x + 5)/2 - sin(6*x + 5)/12", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0908", "stage": "atomic", "k": 1, "integrand": "2*x*cos(15*x + 4)", "integrand_latex": "2 x \\cos{\\left(15 x + 4 \\right)}", "integrand_latex_integral": "\\int 2 x \\cos{\\left(15 x + 4 \\right)} \\, dx", "reference_antiderivative": "2*x*sin(15*x + 4)/15 + 2*cos(15*x + 4)/225", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0909", "stage": "atomic", "k": 1, "integrand": "-4*x*cos(4*x - 11)", "integrand_latex": "- 4 x \\cos{\\left(4 x - 11 \\right)}", "integrand_latex_integral": "\\int - 4 x \\cos{\\left(4 x - 11 \\right)} \\, dx", "reference_antiderivative": "-x*sin(4*x - 11) - cos(4*x - 11)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0910", "stage": "atomic", "k": 1, "integrand": "x*log(15 - 3*x)", "integrand_latex": "x \\log{\\left(15 - 3 x \\right)}", "integrand_latex_integral": "\\int x \\log{\\left(15 - 3 x \\right)} \\, dx", "reference_antiderivative": "x**2*log(15 - 3*x)/2 - x**2/4 - 5*x/2 - 25*log(x - 5)/2", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0911", "stage": "atomic", "k": 1, "integrand": "x*log(7*x + 12)", "integrand_latex": "x \\log{\\left(7 x + 12 \\right)}", "integrand_latex_integral": "\\int x \\log{\\left(7 x + 12 \\right)} \\, dx", "reference_antiderivative": "x**2*log(7*x + 12)/2 - x**2/4 + 6*x/7 - 72*log(7*x + 12)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0912", "stage": "atomic", "k": 1, "integrand": "5*x*sin(13*x + 10)", "integrand_latex": "5 x \\sin{\\left(13 x + 10 \\right)}", "integrand_latex_integral": "\\int 5 x \\sin{\\left(13 x + 10 \\right)} \\, dx", "reference_antiderivative": "-5*x*cos(13*x + 10)/13 + 5*sin(13*x + 10)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0913", "stage": "atomic", "k": 1, "integrand": "-5*x*sin(15*x + 12)", "integrand_latex": "- 5 x \\sin{\\left(15 x + 12 \\right)}", "integrand_latex_integral": "\\int - 5 x \\sin{\\left(15 x + 12 \\right)} \\, dx", "reference_antiderivative": "x*cos(15*x + 12)/3 - sin(15*x + 12)/45", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0914", "stage": "atomic", "k": 1, "integrand": "4*x*log(10*x + 3)", "integrand_latex": "4 x \\log{\\left(10 x + 3 \\right)}", "integrand_latex_integral": "\\int 4 x \\log{\\left(10 x + 3 \\right)} \\, dx", "reference_antiderivative": "2*x**2*log(10*x + 3) - x**2 + 3*x/5 - 9*log(10*x + 3)/50", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0915", "stage": "atomic", "k": 1, "integrand": "x*atan(9*x - 4)", "integrand_latex": "x \\operatorname{atan}{\\left(9 x - 4 \\right)}", "integrand_latex_integral": "\\int x \\operatorname{atan}{\\left(9 x - 4 \\right)} \\, dx", "reference_antiderivative": "x**2*atan(9*x - 4)/2 - x/18 - 2*log(81*x**2 - 72*x + 17)/81 - 5*atan(9*x - 4)/54", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0916", "stage": "atomic", "k": 1, "integrand": "5*x*sin(13*x + 11)", "integrand_latex": "5 x \\sin{\\left(13 x + 11 \\right)}", "integrand_latex_integral": "\\int 5 x \\sin{\\left(13 x + 11 \\right)} \\, dx", "reference_antiderivative": "-5*x*cos(13*x + 11)/13 + 5*sin(13*x + 11)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0917", "stage": "atomic", "k": 1, "integrand": "2*x*log(13 - 12*x)", "integrand_latex": "2 x \\log{\\left(13 - 12 x \\right)}", "integrand_latex_integral": "\\int 2 x \\log{\\left(13 - 12 x \\right)} \\, dx", "reference_antiderivative": "x**2*log(13 - 12*x) - x**2/2 - 13*x/12 - 169*log(12*x - 13)/144", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0918", "stage": "atomic", "k": 1, "integrand": "-4*x*cos(7*x - 5)", "integrand_latex": "- 4 x \\cos{\\left(7 x - 5 \\right)}", "integrand_latex_integral": "\\int - 4 x \\cos{\\left(7 x - 5 \\right)} \\, dx", "reference_antiderivative": "-4*x*sin(7*x - 5)/7 - 4*cos(7*x - 5)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0919", "stage": "atomic", "k": 1, "integrand": "5*x*atan(x + 9)", "integrand_latex": "5 x \\operatorname{atan}{\\left(x + 9 \\right)}", "integrand_latex_integral": "\\int 5 x \\operatorname{atan}{\\left(x + 9 \\right)} \\, dx", "reference_antiderivative": "5*x**2*atan(x + 9)/2 - 5*x/2 + 45*log(x**2 + 18*x + 82)/2 - 200*atan(x + 9)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0920", "stage": "atomic", "k": 1, "integrand": "-2*x*cos(15*x + 6)", "integrand_latex": "- 2 x \\cos{\\left(15 x + 6 \\right)}", "integrand_latex_integral": "\\int - 2 x \\cos{\\left(15 x + 6 \\right)} \\, dx", "reference_antiderivative": "-2*x*sin(15*x + 6)/15 - 2*cos(15*x + 6)/225", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0921", "stage": "atomic", "k": 1, "integrand": "-4*x*sin(12*x + 2)", "integrand_latex": "- 4 x \\sin{\\left(12 x + 2 \\right)}", "integrand_latex_integral": "\\int - 4 x \\sin{\\left(12 x + 2 \\right)} \\, dx", "reference_antiderivative": "x*cos(12*x + 2)/3 - sin(12*x + 2)/36", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0922", "stage": "atomic", "k": 1, "integrand": "5*x*log(6*x + 5)", "integrand_latex": "5 x \\log{\\left(6 x + 5 \\right)}", "integrand_latex_integral": "\\int 5 x \\log{\\left(6 x + 5 \\right)} \\, dx", "reference_antiderivative": "5*x**2*log(6*x + 5)/2 - 5*x**2/4 + 25*x/12 - 125*log(6*x + 5)/72", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0923", "stage": "atomic", "k": 1, "integrand": "3*x*exp(13*x + 4)", "integrand_latex": "3 x e^{13 x + 4}", "integrand_latex_integral": "\\int 3 x e^{13 x + 4} \\, dx", "reference_antiderivative": "(39*x - 3)*exp(13*x + 4)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0924", "stage": "atomic", "k": 1, "integrand": "-3*x*log(x + 12)", "integrand_latex": "- 3 x \\log{\\left(x + 12 \\right)}", "integrand_latex_integral": "\\int - 3 x \\log{\\left(x + 12 \\right)} \\, dx", "reference_antiderivative": "-3*x**2*log(x + 12)/2 + 3*x**2/4 - 18*x + 216*log(x + 12)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0925", "stage": "atomic", "k": 1, "integrand": "-3*x*log(9 - 13*x)", "integrand_latex": "- 3 x \\log{\\left(9 - 13 x \\right)}", "integrand_latex_integral": "\\int - 3 x \\log{\\left(9 - 13 x \\right)} \\, dx", "reference_antiderivative": "-3*x**2*log(9 - 13*x)/2 + 3*x**2/4 + 27*x/26 + 243*log(13*x - 9)/338", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0926", "stage": "atomic", "k": 1, "integrand": "x*sin(14*x - 1)", "integrand_latex": "x \\sin{\\left(14 x - 1 \\right)}", "integrand_latex_integral": "\\int x \\sin{\\left(14 x - 1 \\right)} \\, dx", "reference_antiderivative": "-x*cos(14*x - 1)/14 + sin(14*x - 1)/196", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0927", "stage": "atomic", "k": 1, "integrand": "-x*sin(3*x - 11)", "integrand_latex": "- x \\sin{\\left(3 x - 11 \\right)}", "integrand_latex_integral": "\\int - x \\sin{\\left(3 x - 11 \\right)} \\, dx", "reference_antiderivative": "x*cos(3*x - 11)/3 - sin(3*x - 11)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0928", "stage": "atomic", "k": 1, "integrand": "2*x*log(10*x + 3)", "integrand_latex": "2 x \\log{\\left(10 x + 3 \\right)}", "integrand_latex_integral": "\\int 2 x \\log{\\left(10 x + 3 \\right)} \\, dx", "reference_antiderivative": "x**2*log(10*x + 3) - x**2/2 + 3*x/10 - 9*log(10*x + 3)/100", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0929", "stage": "atomic", "k": 1, "integrand": "2*x*exp(-x - 5)", "integrand_latex": "2 x e^{- x - 5}", "integrand_latex_integral": "\\int 2 x e^{- x - 5} \\, dx", "reference_antiderivative": "(-2*x - 2)*exp(-x - 5)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0930", "stage": "atomic", "k": 1, "integrand": "5*x*log(-15*x - 12)", "integrand_latex": "5 x \\log{\\left(- 15 x - 12 \\right)}", "integrand_latex_integral": "\\int 5 x \\log{\\left(- 15 x - 12 \\right)} \\, dx", "reference_antiderivative": "5*x**2*log(-15*x - 12)/2 - 5*x**2/4 + 2*x - 8*log(5*x + 4)/5", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0931", "stage": "atomic", "k": 1, "integrand": "3*x*exp(2*x - 15)", "integrand_latex": "3 x e^{2 x - 15}", "integrand_latex_integral": "\\int 3 x e^{2 x - 15} \\, dx", "reference_antiderivative": "(6*x - 3)*exp(2*x - 15)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0932", "stage": "atomic", "k": 1, "integrand": "4*x*atan(5*x - 6)", "integrand_latex": "4 x \\operatorname{atan}{\\left(5 x - 6 \\right)}", "integrand_latex_integral": "\\int 4 x \\operatorname{atan}{\\left(5 x - 6 \\right)} \\, dx", "reference_antiderivative": "2*x**2*atan(5*x - 6) - 2*x/5 - 12*log(25*x**2 - 60*x + 37)/25 - 14*atan(5*x - 6)/5", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0933", "stage": "atomic", "k": 1, "integrand": "5*x*cos(6*x - 1)", "integrand_latex": "5 x \\cos{\\left(6 x - 1 \\right)}", "integrand_latex_integral": "\\int 5 x \\cos{\\left(6 x - 1 \\right)} \\, dx", "reference_antiderivative": "5*x*sin(6*x - 1)/6 + 5*cos(6*x - 1)/36", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0934", "stage": "atomic", "k": 1, "integrand": "-5*x*log(11*x - 8)", "integrand_latex": "- 5 x \\log{\\left(11 x - 8 \\right)}", "integrand_latex_integral": "\\int - 5 x \\log{\\left(11 x - 8 \\right)} \\, dx", "reference_antiderivative": "-5*x**2*log(11*x - 8)/2 + 5*x**2/4 + 20*x/11 + 160*log(11*x - 8)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0935", "stage": "atomic", "k": 1, "integrand": "4*x*cos(4*x)", "integrand_latex": "4 x \\cos{\\left(4 x \\right)}", "integrand_latex_integral": "\\int 4 x \\cos{\\left(4 x \\right)} \\, dx", "reference_antiderivative": "x*sin(4*x) + cos(4*x)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0936", "stage": "atomic", "k": 1, "integrand": "4*x*sin(12*x - 9)", "integrand_latex": "4 x \\sin{\\left(12 x - 9 \\right)}", "integrand_latex_integral": "\\int 4 x \\sin{\\left(12 x - 9 \\right)} \\, dx", "reference_antiderivative": "-x*cos(12*x - 9)/3 + sin(12*x - 9)/36", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0937", "stage": "atomic", "k": 1, "integrand": "5*x*cos(15*x + 10)", "integrand_latex": "5 x \\cos{\\left(15 x + 10 \\right)}", "integrand_latex_integral": "\\int 5 x \\cos{\\left(15 x + 10 \\right)} \\, dx", "reference_antiderivative": "x*sin(15*x + 10)/3 + cos(15*x + 10)/45", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0938", "stage": "atomic", "k": 1, "integrand": "4*x*sin(14*x - 13)", "integrand_latex": "4 x \\sin{\\left(14 x - 13 \\right)}", "integrand_latex_integral": "\\int 4 x \\sin{\\left(14 x - 13 \\right)} \\, dx", "reference_antiderivative": "-2*x*cos(14*x - 13)/7 + sin(14*x - 13)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0939", "stage": "atomic", "k": 1, "integrand": "-x*atan(12*x + 7)", "integrand_latex": "- x \\operatorname{atan}{\\left(12 x + 7 \\right)}", "integrand_latex_integral": "\\int - x \\operatorname{atan}{\\left(12 x + 7 \\right)} \\, dx", "reference_antiderivative": "-x**2*atan(12*x + 7)/2 + x/24 - 7*log(72*x**2 + 84*x + 25)/288 + atan(12*x + 7)/6", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0940", "stage": "atomic", "k": 1, "integrand": "-4*x*log(14*x + 12)", "integrand_latex": "- 4 x \\log{\\left(14 x + 12 \\right)}", "integrand_latex_integral": "\\int - 4 x \\log{\\left(14 x + 12 \\right)} \\, dx", "reference_antiderivative": "-2*x**2*log(14*x + 12) + x**2 - 12*x/7 + 72*log(7*x + 6)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0941", "stage": "atomic", "k": 1, "integrand": "-2*x*exp(7*x - 5)", "integrand_latex": "- 2 x e^{7 x - 5}", "integrand_latex_integral": "\\int - 2 x e^{7 x - 5} \\, dx", "reference_antiderivative": "(2 - 14*x)*exp(7*x - 5)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0942", "stage": "atomic", "k": 1, "integrand": "-5*x*atan(14*x + 5)", "integrand_latex": "- 5 x \\operatorname{atan}{\\left(14 x + 5 \\right)}", "integrand_latex_integral": "\\int - 5 x \\operatorname{atan}{\\left(14 x + 5 \\right)} \\, dx", "reference_antiderivative": "-5*x**2*atan(14*x + 5)/2 + 5*x/28 - 25*log(98*x**2 + 70*x + 13)/392 + 15*atan(14*x + 5)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0943", "stage": "atomic", "k": 1, "integrand": "-2*x*atan(x - 6)", "integrand_latex": "- 2 x \\operatorname{atan}{\\left(x - 6 \\right)}", "integrand_latex_integral": "\\int - 2 x \\operatorname{atan}{\\left(x - 6 \\right)} \\, dx", "reference_antiderivative": "-x**2*atan(x - 6) + x + 6*log(x**2 - 12*x + 37) + 35*atan(x - 6)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0944", "stage": "atomic", "k": 1, "integrand": "-3*x*exp(15*x)", "integrand_latex": "- 3 x e^{15 x}", "integrand_latex_integral": "\\int - 3 x e^{15 x} \\, dx", "reference_antiderivative": "(1 - 15*x)*exp(15*x)/75", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0945", "stage": "atomic", "k": 1, "integrand": "-5*x*log(2*x + 14)", "integrand_latex": "- 5 x \\log{\\left(2 x + 14 \\right)}", "integrand_latex_integral": "\\int - 5 x \\log{\\left(2 x + 14 \\right)} \\, dx", "reference_antiderivative": "-5*x**2*log(2*x + 14)/2 + 5*x**2/4 - 35*x/2 + 245*log(x + 7)/2", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0946", "stage": "atomic", "k": 1, "integrand": "2*x*sin(14*x + 1)", "integrand_latex": "2 x \\sin{\\left(14 x + 1 \\right)}", "integrand_latex_integral": "\\int 2 x \\sin{\\left(14 x + 1 \\right)} \\, dx", "reference_antiderivative": "-x*cos(14*x + 1)/7 + sin(14*x + 1)/98", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0947", "stage": "atomic", "k": 1, "integrand": "-3*x*sin(8*x + 11)", "integrand_latex": "- 3 x \\sin{\\left(8 x + 11 \\right)}", "integrand_latex_integral": "\\int - 3 x \\sin{\\left(8 x + 11 \\right)} \\, dx", "reference_antiderivative": "3*x*cos(8*x + 11)/8 - 3*sin(8*x + 11)/64", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0948", "stage": "atomic", "k": 1, "integrand": "5*x*cos(4*x + 4)", "integrand_latex": "5 x \\cos{\\left(4 x + 4 \\right)}", "integrand_latex_integral": "\\int 5 x \\cos{\\left(4 x + 4 \\right)} \\, dx", "reference_antiderivative": "5*x*sin(4*x + 4)/4 + 5*cos(4*x + 4)/16", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0949", "stage": "atomic", "k": 1, "integrand": "-x*sin(2*x - 4)", "integrand_latex": "- x \\sin{\\left(2 x - 4 \\right)}", "integrand_latex_integral": "\\int - x \\sin{\\left(2 x - 4 \\right)} \\, dx", "reference_antiderivative": "x*cos(2*x - 4)/2 - sin(2*x - 4)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0950", "stage": "atomic", "k": 1, "integrand": "x*sin(x - 10)", "integrand_latex": "x \\sin{\\left(x - 10 \\right)}", "integrand_latex_integral": "\\int x \\sin{\\left(x - 10 \\right)} \\, dx", "reference_antiderivative": "-x*cos(x - 10) + sin(x - 10)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0951", "stage": "atomic", "k": 1, "integrand": "4*x*atan(7*x + 13)", "integrand_latex": "4 x \\operatorname{atan}{\\left(7 x + 13 \\right)}", "integrand_latex_integral": "\\int 4 x \\operatorname{atan}{\\left(7 x + 13 \\right)} \\, dx", "reference_antiderivative": "2*x**2*atan(7*x + 13) - 2*x/7 + 26*log(49*x**2 + 182*x + 170)/49 - 48*atan(7*x + 13)/7", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0952", "stage": "atomic", "k": 1, "integrand": "3*x*atan(12*x - 5)", "integrand_latex": "3 x \\operatorname{atan}{\\left(12 x - 5 \\right)}", "integrand_latex_integral": "\\int 3 x \\operatorname{atan}{\\left(12 x - 5 \\right)} \\, dx", "reference_antiderivative": "3*x**2*atan(12*x - 5)/2 - x/8 - 5*log(72*x**2 - 60*x + 13)/96 - atan(12*x - 5)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0953", "stage": "atomic", "k": 1, "integrand": "-2*x*cos(9*x - 4)", "integrand_latex": "- 2 x \\cos{\\left(9 x - 4 \\right)}", "integrand_latex_integral": "\\int - 2 x \\cos{\\left(9 x - 4 \\right)} \\, dx", "reference_antiderivative": "-2*x*sin(9*x - 4)/9 - 2*cos(9*x - 4)/81", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0954", "stage": "atomic", "k": 1, "integrand": "-5*x*sin(11*x - 7)", "integrand_latex": "- 5 x \\sin{\\left(11 x - 7 \\right)}", "integrand_latex_integral": "\\int - 5 x \\sin{\\left(11 x - 7 \\right)} \\, dx", "reference_antiderivative": "5*x*cos(11*x - 7)/11 - 5*sin(11*x - 7)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0955", "stage": "atomic", "k": 1, "integrand": "5*x*exp(7 - 5*x)", "integrand_latex": "5 x e^{7 - 5 x}", "integrand_latex_integral": "\\int 5 x e^{7 - 5 x} \\, dx", "reference_antiderivative": "(-5*x - 1)*exp(7 - 5*x)/5", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0956", "stage": "atomic", "k": 1, "integrand": "3*x*log(3*x + 3)", "integrand_latex": "3 x \\log{\\left(3 x + 3 \\right)}", "integrand_latex_integral": "\\int 3 x \\log{\\left(3 x + 3 \\right)} \\, dx", "reference_antiderivative": "3*x**2*log(3*x + 3)/2 - 3*x**2/4 + 3*x/2 - 3*log(x + 1)/2", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0957", "stage": "atomic", "k": 1, "integrand": "3*x*log(13 - 6*x)", "integrand_latex": "3 x \\log{\\left(13 - 6 x \\right)}", "integrand_latex_integral": "\\int 3 x \\log{\\left(13 - 6 x \\right)} \\, dx", "reference_antiderivative": "3*x**2*log(13 - 6*x)/2 - 3*x**2/4 - 13*x/4 - 169*log(6*x - 13)/24", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0958", "stage": "atomic", "k": 1, "integrand": "3*x*log(-12*x - 15)", "integrand_latex": "3 x \\log{\\left(- 12 x - 15 \\right)}", "integrand_latex_integral": "\\int 3 x \\log{\\left(- 12 x - 15 \\right)} \\, dx", "reference_antiderivative": "3*x**2*log(-12*x - 15)/2 - 3*x**2/4 + 15*x/8 - 75*log(4*x + 5)/32", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0959", "stage": "atomic", "k": 1, "integrand": "5*x*cos(14*x + 9)", "integrand_latex": "5 x \\cos{\\left(14 x + 9 \\right)}", "integrand_latex_integral": "\\int 5 x \\cos{\\left(14 x + 9 \\right)} \\, dx", "reference_antiderivative": "5*x*sin(14*x + 9)/14 + 5*cos(14*x + 9)/196", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0960", "stage": "atomic", "k": 1, "integrand": "-3*x*cos(6*x - 6)", "integrand_latex": "- 3 x \\cos{\\left(6 x - 6 \\right)}", "integrand_latex_integral": "\\int - 3 x \\cos{\\left(6 x - 6 \\right)} \\, dx", "reference_antiderivative": "-x*sin(6*x - 6)/2 - cos(6*x - 6)/12", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0961", "stage": "atomic", "k": 1, "integrand": "-5*x*cos(7*x + 10)", "integrand_latex": "- 5 x \\cos{\\left(7 x + 10 \\right)}", "integrand_latex_integral": "\\int - 5 x \\cos{\\left(7 x + 10 \\right)} \\, dx", "reference_antiderivative": "-5*x*sin(7*x + 10)/7 - 5*cos(7*x + 10)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0962", "stage": "atomic", "k": 1, "integrand": "3*x*log(-14*x - 4)", "integrand_latex": "3 x \\log{\\left(- 14 x - 4 \\right)}", "integrand_latex_integral": "\\int 3 x \\log{\\left(- 14 x - 4 \\right)} \\, dx", "reference_antiderivative": "3*x**2*log(-14*x - 4)/2 - 3*x**2/4 + 3*x/7 - 6*log(7*x + 2)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0963", "stage": "atomic", "k": 1, "integrand": "5*x*sin(8*x + 2)", "integrand_latex": "5 x \\sin{\\left(8 x + 2 \\right)}", "integrand_latex_integral": "\\int 5 x \\sin{\\left(8 x + 2 \\right)} \\, dx", "reference_antiderivative": "-5*x*cos(8*x + 2)/8 + 5*sin(8*x + 2)/64", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0964", "stage": "atomic", "k": 1, "integrand": "-3*x*atan(3*x + 8)", "integrand_latex": "- 3 x \\operatorname{atan}{\\left(3 x + 8 \\right)}", "integrand_latex_integral": "\\int - 3 x \\operatorname{atan}{\\left(3 x + 8 \\right)} \\, dx", "reference_antiderivative": "-3*x**2*atan(3*x + 8)/2 + x/2 - 4*log(9*x**2 + 48*x + 65)/3 + 21*atan(3*x + 8)/2", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0965", "stage": "atomic", "k": 1, "integrand": "-x*exp(7*x + 6)", "integrand_latex": "- x e^{7 x + 6}", "integrand_latex_integral": "\\int - x e^{7 x + 6} \\, dx", "reference_antiderivative": "(1 - 7*x)*exp(7*x + 6)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0966", "stage": "atomic", "k": 1, "integrand": "x*cos(2*x - 15)", "integrand_latex": "x \\cos{\\left(2 x - 15 \\right)}", "integrand_latex_integral": "\\int x \\cos{\\left(2 x - 15 \\right)} \\, dx", "reference_antiderivative": "x*sin(2*x - 15)/2 + cos(2*x - 15)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0967", "stage": "atomic", "k": 1, "integrand": "-5*x*cos(15*x - 8)", "integrand_latex": "- 5 x \\cos{\\left(15 x - 8 \\right)}", "integrand_latex_integral": "\\int - 5 x \\cos{\\left(15 x - 8 \\right)} \\, dx", "reference_antiderivative": "-x*sin(15*x - 8)/3 - cos(15*x - 8)/45", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0968", "stage": "atomic", "k": 1, "integrand": "3*x*sin(8*x + 4)", "integrand_latex": "3 x \\sin{\\left(8 x + 4 \\right)}", "integrand_latex_integral": "\\int 3 x \\sin{\\left(8 x + 4 \\right)} \\, dx", "reference_antiderivative": "-3*x*cos(8*x + 4)/8 + 3*sin(8*x + 4)/64", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0969", "stage": "atomic", "k": 1, "integrand": "2*x*sin(6*x + 1)", "integrand_latex": "2 x \\sin{\\left(6 x + 1 \\right)}", "integrand_latex_integral": "\\int 2 x \\sin{\\left(6 x + 1 \\right)} \\, dx", "reference_antiderivative": "-x*cos(6*x + 1)/3 + sin(6*x + 1)/18", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0970", "stage": "atomic", "k": 1, "integrand": "-4*x*log(-3*x - 14)", "integrand_latex": "- 4 x \\log{\\left(- 3 x - 14 \\right)}", "integrand_latex_integral": "\\int - 4 x \\log{\\left(- 3 x - 14 \\right)} \\, dx", "reference_antiderivative": "-2*x**2*log(-3*x - 14) + x**2 - 28*x/3 + 392*log(3*x + 14)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0971", "stage": "atomic", "k": 1, "integrand": "x*atan(11*x + 10)", "integrand_latex": "x \\operatorname{atan}{\\left(11 x + 10 \\right)}", "integrand_latex_integral": "\\int x \\operatorname{atan}{\\left(11 x + 10 \\right)} \\, dx", "reference_antiderivative": "x**2*atan(11*x + 10)/2 - x/22 + 5*log(121*x**2 + 220*x + 101)/121 - 9*atan(11*x + 10)/22", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0972", "stage": "atomic", "k": 1, "integrand": "5*x*sin(5*x + 1)", "integrand_latex": "5 x \\sin{\\left(5 x + 1 \\right)}", "integrand_latex_integral": "\\int 5 x \\sin{\\left(5 x + 1 \\right)} \\, dx", "reference_antiderivative": "-x*cos(5*x + 1) + sin(5*x + 1)/5", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0973", "stage": "atomic", "k": 1, "integrand": "-4*x*atan(14*x - 9)", "integrand_latex": "- 4 x \\operatorname{atan}{\\left(14 x - 9 \\right)}", "integrand_latex_integral": "\\int - 4 x \\operatorname{atan}{\\left(14 x - 9 \\right)} \\, dx", "reference_antiderivative": "-2*x**2*atan(14*x - 9) + x/7 + 9*log(98*x**2 - 126*x + 41)/98 + 40*atan(14*x - 9)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0974", "stage": "atomic", "k": 1, "integrand": "-x*atan(10*x + 3)", "integrand_latex": "- x \\operatorname{atan}{\\left(10 x + 3 \\right)}", "integrand_latex_integral": "\\int - x \\operatorname{atan}{\\left(10 x + 3 \\right)} \\, dx", "reference_antiderivative": "-x**2*atan(10*x + 3)/2 + x/20 - 3*log(10*x**2 + 6*x + 1)/200 + atan(10*x + 3)/25", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0975", "stage": "atomic", "k": 1, "integrand": "-3*x*sin(8*x - 15)", "integrand_latex": "- 3 x \\sin{\\left(8 x - 15 \\right)}", "integrand_latex_integral": "\\int - 3 x \\sin{\\left(8 x - 15 \\right)} \\, dx", "reference_antiderivative": "3*x*cos(8*x - 15)/8 - 3*sin(8*x - 15)/64", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0976", "stage": "atomic", "k": 1, "integrand": "-3*x*atan(10*x + 2)", "integrand_latex": "- 3 x \\operatorname{atan}{\\left(10 x + 2 \\right)}", "integrand_latex_integral": "\\int - 3 x \\operatorname{atan}{\\left(10 x + 2 \\right)} \\, dx", "reference_antiderivative": "-3*x**2*atan(10*x + 2)/2 + 3*x/20 - 3*log(20*x**2 + 8*x + 1)/100 + 9*atan(10*x + 2)/200", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0977", "stage": "atomic", "k": 1, "integrand": "4*x*sin(4*x + 8)", "integrand_latex": "4 x \\sin{\\left(4 x + 8 \\right)}", "integrand_latex_integral": "\\int 4 x \\sin{\\left(4 x + 8 \\right)} \\, dx", "reference_antiderivative": "-x*cos(4*x + 8) + sin(4*x + 8)/4", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0978", "stage": "atomic", "k": 1, "integrand": "x*atan(9*x - 15)", "integrand_latex": "x \\operatorname{atan}{\\left(9 x - 15 \\right)}", "integrand_latex_integral": "\\int x \\operatorname{atan}{\\left(9 x - 15 \\right)} \\, dx", "reference_antiderivative": "x**2*atan(9*x - 15)/2 - x/18 - 5*log(81*x**2 - 270*x + 226)/54 - 112*atan(9*x - 15)/81", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0979", "stage": "atomic", "k": 1, "integrand": "3*x*exp(11*x + 9)", "integrand_latex": "3 x e^{11 x + 9}", "integrand_latex_integral": "\\int 3 x e^{11 x + 9} \\, dx", "reference_antiderivative": "(33*x - 3)*exp(11*x + 9)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0980", "stage": "atomic", "k": 1, "integrand": "-2*x*atan(8*x - 13)", "integrand_latex": "- 2 x \\operatorname{atan}{\\left(8 x - 13 \\right)}", "integrand_latex_integral": "\\int - 2 x \\operatorname{atan}{\\left(8 x - 13 \\right)} \\, dx", "reference_antiderivative": "-x**2*atan(8*x - 13) + x/8 + 13*log(32*x**2 - 104*x + 85)/64 + 21*atan(8*x - 13)/8", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0981", "stage": "atomic", "k": 1, "integrand": "-2*x*cos(15*x - 14)", "integrand_latex": "- 2 x \\cos{\\left(15 x - 14 \\right)}", "integrand_latex_integral": "\\int - 2 x \\cos{\\left(15 x - 14 \\right)} \\, dx", "reference_antiderivative": "-2*x*sin(15*x - 14)/15 - 2*cos(15*x - 14)/225", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0982", "stage": "atomic", "k": 1, "integrand": "4*x*atan(3*x + 7)", "integrand_latex": "4 x \\operatorname{atan}{\\left(3 x + 7 \\right)}", "integrand_latex_integral": "\\int 4 x \\operatorname{atan}{\\left(3 x + 7 \\right)} \\, dx", "reference_antiderivative": "2*x**2*atan(3*x + 7) - 2*x/3 + 14*log(9*x**2 + 42*x + 50)/9 - 32*atan(3*x + 7)/3", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0983", "stage": "atomic", "k": 1, "integrand": "-5*x*cos(14*x + 1)", "integrand_latex": "- 5 x \\cos{\\left(14 x + 1 \\right)}", "integrand_latex_integral": "\\int - 5 x \\cos{\\left(14 x + 1 \\right)} \\, dx", "reference_antiderivative": "-5*x*sin(14*x + 1)/14 - 5*cos(14*x + 1)/196", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0984", "stage": "atomic", "k": 1, "integrand": "3*x*exp(-x)", "integrand_latex": "3 x e^{- x}", "integrand_latex_integral": "\\int 3 x e^{- x} \\, dx", "reference_antiderivative": "(-3*x - 3)*exp(-x)", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0985", "stage": "atomic", "k": 1, "integrand": "-5*x*atan(9*x + 5)", "integrand_latex": "- 5 x \\operatorname{atan}{\\left(9 x + 5 \\right)}", "integrand_latex_integral": "\\int - 5 x \\operatorname{atan}{\\left(9 x + 5 \\right)} \\, dx", "reference_antiderivative": "-5*x**2*atan(9*x + 5)/2 + 5*x/18 - 25*log(81*x**2 + 90*x + 26)/162 + 20*atan(9*x + 5)/27", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0986", "stage": "atomic", "k": 1, "integrand": "4*x*atan(10*x - 15)", "integrand_latex": "4 x \\operatorname{atan}{\\left(10 x - 15 \\right)}", "integrand_latex_integral": "\\int 4 x \\operatorname{atan}{\\left(10 x - 15 \\right)} \\, dx", "reference_antiderivative": "2*x**2*atan(10*x - 15) - x/5 - 3*log(50*x**2 - 150*x + 113)/10 - 112*atan(10*x - 15)/25", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0987", "stage": "atomic", "k": 1, "integrand": "-5*x*sin(13*x + 9)", "integrand_latex": "- 5 x \\sin{\\left(13 x + 9 \\right)}", "integrand_latex_integral": "\\int - 5 x \\sin{\\left(13 x + 9 \\right)} \\, dx", "reference_antiderivative": "5*x*cos(13*x + 9)/13 - 5*sin(13*x + 9)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0988", "stage": "atomic", "k": 1, "integrand": "x*sin(11*x - 12)", "integrand_latex": "x \\sin{\\left(11 x - 12 \\right)}", "integrand_latex_integral": "\\int x \\sin{\\left(11 x - 12 \\right)} \\, dx", "reference_antiderivative": "-x*cos(11*x - 12)/11 + sin(11*x - 12)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0989", "stage": "atomic", "k": 1, "integrand": "x*exp(5*x + 11)", "integrand_latex": "x e^{5 x + 11}", "integrand_latex_integral": "\\int x e^{5 x + 11} \\, dx", "reference_antiderivative": "(5*x - 1)*exp(5*x + 11)/25", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0990", "stage": "atomic", "k": 1, "integrand": "-3*x*cos(15*x + 1)", "integrand_latex": "- 3 x \\cos{\\left(15 x + 1 \\right)}", "integrand_latex_integral": "\\int - 3 x \\cos{\\left(15 x + 1 \\right)} \\, dx", "reference_antiderivative": "-x*sin(15*x + 1)/5 - cos(15*x + 1)/75", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0991", "stage": "atomic", "k": 1, "integrand": "-4*x*cos(14*x + 10)", "integrand_latex": "- 4 x \\cos{\\left(14 x + 10 \\right)}", "integrand_latex_integral": "\\int - 4 x \\cos{\\left(14 x + 10 \\right)} \\, dx", "reference_antiderivative": "-2*x*sin(14*x + 10)/7 - cos(14*x + 10)/49", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0992", "stage": "atomic", "k": 1, "integrand": "4*x*cos(11*x - 8)", "integrand_latex": "4 x \\cos{\\left(11 x - 8 \\right)}", "integrand_latex_integral": "\\int 4 x \\cos{\\left(11 x - 8 \\right)} \\, dx", "reference_antiderivative": "4*x*sin(11*x - 8)/11 + 4*cos(11*x - 8)/121", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0993", "stage": "atomic", "k": 1, "integrand": "2*x*log(5*x - 3)", "integrand_latex": "2 x \\log{\\left(5 x - 3 \\right)}", "integrand_latex_integral": "\\int 2 x \\log{\\left(5 x - 3 \\right)} \\, dx", "reference_antiderivative": "x**2*log(5*x - 3) - x**2/2 - 3*x/5 - 9*log(5*x - 3)/25", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0994", "stage": "atomic", "k": 1, "integrand": "x*atan(6*x - 12)", "integrand_latex": "x \\operatorname{atan}{\\left(6 x - 12 \\right)}", "integrand_latex_integral": "\\int x \\operatorname{atan}{\\left(6 x - 12 \\right)} \\, dx", "reference_antiderivative": "x**2*atan(6*x - 12)/2 - x/12 - log(36*x**2 - 144*x + 145)/6 - 143*atan(6*x - 12)/72", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0995", "stage": "atomic", "k": 1, "integrand": "-4*x*atan(13*x - 9)", "integrand_latex": "- 4 x \\operatorname{atan}{\\left(13 x - 9 \\right)}", "integrand_latex_integral": "\\int - 4 x \\operatorname{atan}{\\left(13 x - 9 \\right)} \\, dx", "reference_antiderivative": "-2*x**2*atan(13*x - 9) + 2*x/13 + 18*log(169*x**2 - 234*x + 82)/169 + 160*atan(13*x - 9)/169", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0996", "stage": "atomic", "k": 1, "integrand": "4*x*atan(4*x - 14)", "integrand_latex": "4 x \\operatorname{atan}{\\left(4 x - 14 \\right)}", "integrand_latex_integral": "\\int 4 x \\operatorname{atan}{\\left(4 x - 14 \\right)} \\, dx", "reference_antiderivative": "2*x**2*atan(4*x - 14) - x/2 - 7*log(16*x**2 - 112*x + 197)/4 - 195*atan(4*x - 14)/8", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0997", "stage": "atomic", "k": 1, "integrand": "5*x*exp(4 - 6*x)", "integrand_latex": "5 x e^{4 - 6 x}", "integrand_latex_integral": "\\int 5 x e^{4 - 6 x} \\, dx", "reference_antiderivative": "(-30*x - 5)*exp(4 - 6*x)/36", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0998", "stage": "atomic", "k": 1, "integrand": "2*x*exp(-3*x - 3)", "integrand_latex": "2 x e^{- 3 x - 3}", "integrand_latex_integral": "\\int 2 x e^{- 3 x - 3} \\, dx", "reference_antiderivative": "(-6*x - 2)*exp(-3*x - 3)/9", "category": "integration_primitive", "variable": "x"}
{"id": "atom-0999", "stage": "atomic", "k": 1, "integrand": "3*x*log(-8*x - 11)", "integrand_latex": "3 x \\log{\\left(- 8 x - 11 \\right)}", "integrand_latex_integral": "\\int 3 x \\log{\\left(- 8 x - 11 \\right)} \\, dx", "reference_antiderivative": "3*x**2*log(-8*x - 11)/2 - 3*x**2/4 + 33*x/16 - 363*log(8*x + 11)/128", "category": "integration_primitive", "variable": "x"}