Datasets:
chenpanli
/
integrals

Dataset card Data Studio Files
xet
 Community
id
stringlengths
9
9
stage
stringclasses
1 value
k
int64
1
1
integrand
stringlengths
2
20
integrand_latex
stringlengths
3
50
integrand_latex_integral
stringlengths
14
61
reference_antiderivative
stringlengths
3
92
category
stringclasses
5 values
variable
stringclasses
1 value
atom-0100
atomic
1
x**2
x^{2}
\int x^{2} \, dx
x**3/3
polynomial
x
atom-0101
atomic
1
-3/x**14
- \frac{3}{x^{14}}
\int - \frac{3}{x^{14}} \, dx
3/(13*x**13)
polynomial
x
atom-0102
atomic
1
-5*x**13
- 5 x^{13}
\int - 5 x^{13} \, dx
-5*x**14/14
polynomial
x
atom-0103
atomic
1
5/x**8
\frac{5}{x^{8}}
\int \frac{5}{x^{8}} \, dx
-5/(7*x**7)
polynomial
x
atom-0104
atomic
1
3*x**13
3 x^{13}
\int 3 x^{13} \, dx
3*x**14/14
polynomial
x
atom-0105
atomic
1
4*x**8
4 x^{8}
\int 4 x^{8} \, dx
4*x**9/9
polynomial
x
atom-0106
atomic
1
-2*x**12
- 2 x^{12}
\int - 2 x^{12} \, dx
-2*x**13/13
polynomial
x
atom-0107
atomic
1
-3*x**13
- 3 x^{13}
\int - 3 x^{13} \, dx
-3*x**14/14
polynomial
x
atom-0108
atomic
1
x**10
x^{10}
\int x^{10} \, dx
x**11/11
polynomial
x
atom-0109
atomic
1
2/x**8
\frac{2}{x^{8}}
\int \frac{2}{x^{8}} \, dx
-2/(7*x**7)
polynomial
x
atom-0110
atomic
1
2/x**4
\frac{2}{x^{4}}
\int \frac{2}{x^{4}} \, dx
-2/(3*x**3)
polynomial
x
atom-0111
atomic
1
-2/x**8
- \frac{2}{x^{8}}
\int - \frac{2}{x^{8}} \, dx
2/(7*x**7)
polynomial
x
atom-0112
atomic
1
3/x**5
\frac{3}{x^{5}}
\int \frac{3}{x^{5}} \, dx
-3/(4*x**4)
polynomial
x
atom-0113
atomic
1
-3*x**3
- 3 x^{3}
\int - 3 x^{3} \, dx
-3*x**4/4
polynomial
x
atom-0114
atomic
1
x**(-4)
\frac{1}{x^{4}}
\int \frac{1}{x^{4}} \, dx
-1/(3*x**3)
polynomial
x
atom-0115
atomic
1
x**4
x^{4}
\int x^{4} \, dx
x**5/5
polynomial
x
atom-0116
atomic
1
x**(-15)
\frac{1}{x^{15}}
\int \frac{1}{x^{15}} \, dx
-1/(14*x**14)
polynomial
x
atom-0117
atomic
1
5/x**9
\frac{5}{x^{9}}
\int \frac{5}{x^{9}} \, dx
-5/(8*x**8)
polynomial
x
atom-0118
atomic
1
4/x**5
\frac{4}{x^{5}}
\int \frac{4}{x^{5}} \, dx
-1/x**4
polynomial
x
atom-0119
atomic
1
-4*x**8
- 4 x^{8}
\int - 4 x^{8} \, dx
-4*x**9/9
polynomial
x
atom-0120
atomic
1
x**7
x^{7}
\int x^{7} \, dx
x**8/8
polynomial
x
atom-0121
atomic
1
x**6
x^{6}
\int x^{6} \, dx
x**7/7
polynomial
x
atom-0122
atomic
1
-3*x**4
- 3 x^{4}
\int - 3 x^{4} \, dx
-3*x**5/5
polynomial
x
atom-0123
atomic
1
-1/x**6
- \frac{1}{x^{6}}
\int - \frac{1}{x^{6}} \, dx
1/(5*x**5)
polynomial
x
atom-0124
atomic
1
4*x**4
4 x^{4}
\int 4 x^{4} \, dx
4*x**5/5
polynomial
x
atom-0125
atomic
1
2/x
\frac{2}{x}
\int \frac{2}{x} \, dx
2*log(x)
polynomial
x
atom-0126
atomic
1
-3*x**6
- 3 x^{6}
\int - 3 x^{6} \, dx
-3*x**7/7
polynomial
x
atom-0127
atomic
1
-4*x**11
- 4 x^{11}
\int - 4 x^{11} \, dx
-x**12/3
polynomial
x
atom-0128
atomic
1
-2*x**4
- 2 x^{4}
\int - 2 x^{4} \, dx
-2*x**5/5
polynomial
x
atom-0129
atomic
1
5*x**7
5 x^{7}
\int 5 x^{7} \, dx
5*x**8/8
polynomial
x
atom-0130
atomic
1
-3*x**10
- 3 x^{10}
\int - 3 x^{10} \, dx
-3*x**11/11
polynomial
x
atom-0131
atomic
1
-2*x**14
- 2 x^{14}
\int - 2 x^{14} \, dx
-2*x**15/15
polynomial
x
atom-0132
atomic
1
2/x**11
\frac{2}{x^{11}}
\int \frac{2}{x^{11}} \, dx
-1/(5*x**10)
polynomial
x
atom-0133
atomic
1
2*x**4
2 x^{4}
\int 2 x^{4} \, dx
2*x**5/5
polynomial
x
atom-0134
atomic
1
-2*x**11
- 2 x^{11}
\int - 2 x^{11} \, dx
-x**12/6
polynomial
x
atom-0135
atomic
1
3*x**5
3 x^{5}
\int 3 x^{5} \, dx
x**6/2
polynomial
x
atom-0136
atomic
1
2/x**13
\frac{2}{x^{13}}
\int \frac{2}{x^{13}} \, dx
-1/(6*x**12)
polynomial
x
atom-0137
atomic
1
4/x**3
\frac{4}{x^{3}}
\int \frac{4}{x^{3}} \, dx
-2/x**2
polynomial
x
atom-0138
atomic
1
-x**9
- x^{9}
\int - x^{9} \, dx
-x**10/10
polynomial
x
atom-0139
atomic
1
3*x**10
3 x^{10}
\int 3 x^{10} \, dx
3*x**11/11
polynomial
x
atom-0140
atomic
1
5*x**6
5 x^{6}
\int 5 x^{6} \, dx
5*x**7/7
polynomial
x
atom-0141
atomic
1
-3*x**11
- 3 x^{11}
\int - 3 x^{11} \, dx
-x**12/4
polynomial
x
atom-0142
atomic
1
x**3
x^{3}
\int x^{3} \, dx
x**4/4
polynomial
x
atom-0143
atomic
1
-3*x**12
- 3 x^{12}
\int - 3 x^{12} \, dx
-3*x**13/13
polynomial
x
atom-0144
atomic
1
-5/x**7
- \frac{5}{x^{7}}
\int - \frac{5}{x^{7}} \, dx
5/(6*x**6)
polynomial
x
atom-0145
atomic
1
-2/x
- \frac{2}{x}
\int - \frac{2}{x} \, dx
-2*log(x)
polynomial
x
atom-0146
atomic
1
-5*x**15
- 5 x^{15}
\int - 5 x^{15} \, dx
-5*x**16/16
polynomial
x
atom-0147
atomic
1
5/x**13
\frac{5}{x^{13}}
\int \frac{5}{x^{13}} \, dx
-5/(12*x**12)
polynomial
x
atom-0148
atomic
1
-2/x**9
- \frac{2}{x^{9}}
\int - \frac{2}{x^{9}} \, dx
1/(4*x**8)
polynomial
x
atom-0149
atomic
1
4/x**11
\frac{4}{x^{11}}
\int \frac{4}{x^{11}} \, dx
-2/(5*x**10)
polynomial
x
atom-0150
atomic
1
2*x**6
2 x^{6}
\int 2 x^{6} \, dx
2*x**7/7
polynomial
x
atom-0151
atomic
1
-x**3
- x^{3}
\int - x^{3} \, dx
-x**4/4
polynomial
x
atom-0152
atomic
1
-x**12
- x^{12}
\int - x^{12} \, dx
-x**13/13
polynomial
x
atom-0153
atomic
1
-4*x**10
- 4 x^{10}
\int - 4 x^{10} \, dx
-4*x**11/11
polynomial
x
atom-0154
atomic
1
-5/x**4
- \frac{5}{x^{4}}
\int - \frac{5}{x^{4}} \, dx
5/(3*x**3)
polynomial
x
atom-0155
atomic
1
5/x**4
\frac{5}{x^{4}}
\int \frac{5}{x^{4}} \, dx
-5/(3*x**3)
polynomial
x
atom-0156
atomic
1
x**11
x^{11}
\int x^{11} \, dx
x**12/12
polynomial
x
atom-0157
atomic
1
2*x**7
2 x^{7}
\int 2 x^{7} \, dx
x**8/4
polynomial
x
atom-0158
atomic
1
5/x**7
\frac{5}{x^{7}}
\int \frac{5}{x^{7}} \, dx
-5/(6*x**6)
polynomial
x
atom-0159
atomic
1
-1/x**5
- \frac{1}{x^{5}}
\int - \frac{1}{x^{5}} \, dx
1/(4*x**4)
polynomial
x
atom-0160
atomic
1
-4/x**7
- \frac{4}{x^{7}}
\int - \frac{4}{x^{7}} \, dx
2/(3*x**6)
polynomial
x
atom-0161
atomic
1
-2*x**9
- 2 x^{9}
\int - 2 x^{9} \, dx
-x**10/5
polynomial
x
atom-0162
atomic
1
4*x**6
4 x^{6}
\int 4 x^{6} \, dx
4*x**7/7
polynomial
x
atom-0163
atomic
1
4*x**7
4 x^{7}
\int 4 x^{7} \, dx
x**8/2
polynomial
x
atom-0164
atomic
1
3/x**15
\frac{3}{x^{15}}
\int \frac{3}{x^{15}} \, dx
-3/(14*x**14)
polynomial
x
atom-0165
atomic
1
2*x**5
2 x^{5}
\int 2 x^{5} \, dx
x**6/3
polynomial
x
atom-0166
atomic
1
-2/x**6
- \frac{2}{x^{6}}
\int - \frac{2}{x^{6}} \, dx
2/(5*x**5)
polynomial
x
atom-0167
atomic
1
x**8
x^{8}
\int x^{8} \, dx
x**9/9
polynomial
x
atom-0168
atomic
1
2/x**7
\frac{2}{x^{7}}
\int \frac{2}{x^{7}} \, dx
-1/(3*x**6)
polynomial
x
atom-0169
atomic
1
-2/x**12
- \frac{2}{x^{12}}
\int - \frac{2}{x^{12}} \, dx
2/(11*x**11)
polynomial
x
atom-0170
atomic
1
-2/x**4
- \frac{2}{x^{4}}
\int - \frac{2}{x^{4}} \, dx
2/(3*x**3)
polynomial
x
atom-0171
atomic
1
-5*x**7
- 5 x^{7}
\int - 5 x^{7} \, dx
-5*x**8/8
polynomial
x
atom-0172
atomic
1
2/x**12
\frac{2}{x^{12}}
\int \frac{2}{x^{12}} \, dx
-2/(11*x**11)
polynomial
x
atom-0173
atomic
1
4/x**6
\frac{4}{x^{6}}
\int \frac{4}{x^{6}} \, dx
-4/(5*x**5)
polynomial
x
atom-0174
atomic
1
2/x**5
\frac{2}{x^{5}}
\int \frac{2}{x^{5}} \, dx
-1/(2*x**4)
polynomial
x
atom-0175
atomic
1
1/x
\frac{1}{x}
\int \frac{1}{x} \, dx
log(x)
polynomial
x
atom-0176
atomic
1
x**(-6)
\frac{1}{x^{6}}
\int \frac{1}{x^{6}} \, dx
-1/(5*x**5)
polynomial
x
atom-0177
atomic
1
-4/x**10
- \frac{4}{x^{10}}
\int - \frac{4}{x^{10}} \, dx
4/(9*x**9)
polynomial
x
atom-0178
atomic
1
-x**7
- x^{7}
\int - x^{7} \, dx
-x**8/8
polynomial
x
atom-0179
atomic
1
-x**10
- x^{10}
\int - x^{10} \, dx
-x**11/11
polynomial
x
atom-0180
atomic
1
-2/x**2
- \frac{2}{x^{2}}
\int - \frac{2}{x^{2}} \, dx
2/x
polynomial
x
atom-0181
atomic
1
-x**11
- x^{11}
\int - x^{11} \, dx
-x**12/12
polynomial
x
atom-0182
atomic
1
-1/x
- \frac{1}{x}
\int - \frac{1}{x} \, dx
-log(x)
polynomial
x
atom-0183
atomic
1
-1/x**15
- \frac{1}{x^{15}}
\int - \frac{1}{x^{15}} \, dx
1/(14*x**14)
polynomial
x
atom-0184
atomic
1
x**5
x^{5}
\int x^{5} \, dx
x**6/6
polynomial
x
atom-0185
atomic
1
-4/x**4
- \frac{4}{x^{4}}
\int - \frac{4}{x^{4}} \, dx
4/(3*x**3)
polynomial
x
atom-0186
atomic
1
3/x**14
\frac{3}{x^{14}}
\int \frac{3}{x^{14}} \, dx
-3/(13*x**13)
polynomial
x
atom-0187
atomic
1
x**12
x^{12}
\int x^{12} \, dx
x**13/13
polynomial
x
atom-0188
atomic
1
2/x**2
\frac{2}{x^{2}}
\int \frac{2}{x^{2}} \, dx
-2/x
polynomial
x
atom-0189
atomic
1
3/x**4
\frac{3}{x^{4}}
\int \frac{3}{x^{4}} \, dx
-1/x**3
polynomial
x
atom-0190
atomic
1
-5/x**9
- \frac{5}{x^{9}}
\int - \frac{5}{x^{9}} \, dx
5/(8*x**8)
polynomial
x
atom-0191
atomic
1
-3*x**14
- 3 x^{14}
\int - 3 x^{14} \, dx
-x**15/5
polynomial
x
atom-0192
atomic
1
-3/x**6
- \frac{3}{x^{6}}
\int - \frac{3}{x^{6}} \, dx
3/(5*x**5)
polynomial
x
atom-0193
atomic
1
-3/x**3
- \frac{3}{x^{3}}
\int - \frac{3}{x^{3}} \, dx
3/(2*x**2)
polynomial
x
atom-0194
atomic
1
4*x
4 x
\int 4 x \, dx
2*x**2
polynomial
x
atom-0195
atomic
1
-x**8
- x^{8}
\int - x^{8} \, dx
-x**9/9
polynomial
x
atom-0196
atomic
1
2*x**12
2 x^{12}
\int 2 x^{12} \, dx
2*x**13/13
polynomial
x
atom-0197
atomic
1
3/x**3
\frac{3}{x^{3}}
\int \frac{3}{x^{3}} \, dx
-3/(2*x**2)
polynomial
x
atom-0198
atomic
1
x**(-8)
\frac{1}{x^{8}}
\int \frac{1}{x^{8}} \, dx
-1/(7*x**7)
polynomial
x
atom-0199
atomic
1
x**(-14)
\frac{1}{x^{14}}
\int \frac{1}{x^{14}} \, dx
-1/(13*x**13)
polynomial
x