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-0000
atomic
1
-5*x**8
- 5 x^{8}
\int - 5 x^{8} \, dx
-5*x**9/9
polynomial
x
atom-0001
atomic
1
-2/x**11
- \frac{2}{x^{11}}
\int - \frac{2}{x^{11}} \, dx
1/(5*x**10)
polynomial
x
atom-0002
atomic
1
5*x**8
5 x^{8}
\int 5 x^{8} \, dx
5*x**9/9
polynomial
x
atom-0003
atomic
1
-4*x**3
- 4 x^{3}
\int - 4 x^{3} \, dx
-x**4
polynomial
x
atom-0004
atomic
1
-5/x**13
- \frac{5}{x^{13}}
\int - \frac{5}{x^{13}} \, dx
5/(12*x**12)
polynomial
x
atom-0005
atomic
1
3*x**4
3 x^{4}
\int 3 x^{4} \, dx
3*x**5/5
polynomial
x
atom-0006
atomic
1
-2*x**7
- 2 x^{7}
\int - 2 x^{7} \, dx
-x**8/4
polynomial
x
atom-0007
atomic
1
3/x**2
\frac{3}{x^{2}}
\int \frac{3}{x^{2}} \, dx
-3/x
polynomial
x
atom-0008
atomic
1
4/x**7
\frac{4}{x^{7}}
\int \frac{4}{x^{7}} \, dx
-2/(3*x**6)
polynomial
x
atom-0009
atomic
1
-5*x**9
- 5 x^{9}
\int - 5 x^{9} \, dx
-x**10/2
polynomial
x
atom-0010
atomic
1
x**(-5)
\frac{1}{x^{5}}
\int \frac{1}{x^{5}} \, dx
-1/(4*x**4)
polynomial
x
atom-0011
atomic
1
-2*x**15
- 2 x^{15}
\int - 2 x^{15} \, dx
-x**16/8
polynomial
x
atom-0012
atomic
1
-4/x**13
- \frac{4}{x^{13}}
\int - \frac{4}{x^{13}} \, dx
1/(3*x**12)
polynomial
x
atom-0013
atomic
1
2*x**2
2 x^{2}
\int 2 x^{2} \, dx
2*x**3/3
polynomial
x
atom-0014
atomic
1
x**(-13)
\frac{1}{x^{13}}
\int \frac{1}{x^{13}} \, dx
-1/(12*x**12)
polynomial
x
atom-0015
atomic
1
5*x**4
5 x^{4}
\int 5 x^{4} \, dx
x**5
polynomial
x
atom-0016
atomic
1
4/x**9
\frac{4}{x^{9}}
\int \frac{4}{x^{9}} \, dx
-1/(2*x**8)
polynomial
x
atom-0017
atomic
1
-5*x**6
- 5 x^{6}
\int - 5 x^{6} \, dx
-5*x**7/7
polynomial
x
atom-0018
atomic
1
-1/x**13
- \frac{1}{x^{13}}
\int - \frac{1}{x^{13}} \, dx
1/(12*x**12)
polynomial
x
atom-0019
atomic
1
-4/x**3
- \frac{4}{x^{3}}
\int - \frac{4}{x^{3}} \, dx
2/x**2
polynomial
x
atom-0020
atomic
1
5*x**11
5 x^{11}
\int 5 x^{11} \, dx
5*x**12/12
polynomial
x
atom-0021
atomic
1
-2*x**6
- 2 x^{6}
\int - 2 x^{6} \, dx
-2*x**7/7
polynomial
x
atom-0022
atomic
1
5*x**5
5 x^{5}
\int 5 x^{5} \, dx
5*x**6/6
polynomial
x
atom-0023
atomic
1
5/x**10
\frac{5}{x^{10}}
\int \frac{5}{x^{10}} \, dx
-5/(9*x**9)
polynomial
x
atom-0024
atomic
1
-2/x**10
- \frac{2}{x^{10}}
\int - \frac{2}{x^{10}} \, dx
2/(9*x**9)
polynomial
x
atom-0025
atomic
1
-x**14
- x^{14}
\int - x^{14} \, dx
-x**15/15
polynomial
x
atom-0026
atomic
1
3/x**8
\frac{3}{x^{8}}
\int \frac{3}{x^{8}} \, dx
-3/(7*x**7)
polynomial
x
atom-0027
atomic
1
-5/x**8
- \frac{5}{x^{8}}
\int - \frac{5}{x^{8}} \, dx
5/(7*x**7)
polynomial
x
atom-0028
atomic
1
x**(-7)
\frac{1}{x^{7}}
\int \frac{1}{x^{7}} \, dx
-1/(6*x**6)
polynomial
x
atom-0029
atomic
1
4*x**13
4 x^{13}
\int 4 x^{13} \, dx
2*x**14/7
polynomial
x
atom-0030
atomic
1
-2*x**5
- 2 x^{5}
\int - 2 x^{5} \, dx
-x**6/3
polynomial
x
atom-0031
atomic
1
5/x
\frac{5}{x}
\int \frac{5}{x} \, dx
5*log(x)
polynomial
x
atom-0032
atomic
1
-3/x**8
- \frac{3}{x^{8}}
\int - \frac{3}{x^{8}} \, dx
3/(7*x**7)
polynomial
x
atom-0033
atomic
1
3/x**7
\frac{3}{x^{7}}
\int \frac{3}{x^{7}} \, dx
-1/(2*x**6)
polynomial
x
atom-0034
atomic
1
x**13
x^{13}
\int x^{13} \, dx
x**14/14
polynomial
x
atom-0035
atomic
1
-4*x**9
- 4 x^{9}
\int - 4 x^{9} \, dx
-2*x**10/5
polynomial
x
atom-0036
atomic
1
-4/x**11
- \frac{4}{x^{11}}
\int - \frac{4}{x^{11}} \, dx
2/(5*x**10)
polynomial
x
atom-0037
atomic
1
5/x**2
\frac{5}{x^{2}}
\int \frac{5}{x^{2}} \, dx
-5/x
polynomial
x
atom-0038
atomic
1
x**(-3)
\frac{1}{x^{3}}
\int \frac{1}{x^{3}} \, dx
-1/(2*x**2)
polynomial
x
atom-0039
atomic
1
2*x
2 x
\int 2 x \, dx
x**2
polynomial
x
atom-0040
atomic
1
3*x**12
3 x^{12}
\int 3 x^{12} \, dx
3*x**13/13
polynomial
x
atom-0041
atomic
1
3*x**9
3 x^{9}
\int 3 x^{9} \, dx
3*x**10/10
polynomial
x
atom-0042
atomic
1
5/x**5
\frac{5}{x^{5}}
\int \frac{5}{x^{5}} \, dx
-5/(4*x**4)
polynomial
x
atom-0043
atomic
1
x**(-10)
\frac{1}{x^{10}}
\int \frac{1}{x^{10}} \, dx
-1/(9*x**9)
polynomial
x
atom-0044
atomic
1
-x
- x
\int - x \, dx
-x**2/2
polynomial
x
atom-0045
atomic
1
3*x**14
3 x^{14}
\int 3 x^{14} \, dx
x**15/5
polynomial
x
atom-0046
atomic
1
5/x**6
\frac{5}{x^{6}}
\int \frac{5}{x^{6}} \, dx
-1/x**5
polynomial
x
atom-0047
atomic
1
-3*x**2
- 3 x^{2}
\int - 3 x^{2} \, dx
-x**3
polynomial
x
atom-0048
atomic
1
2/x**15
\frac{2}{x^{15}}
\int \frac{2}{x^{15}} \, dx
-1/(7*x**14)
polynomial
x
atom-0049
atomic
1
-1/x**8
- \frac{1}{x^{8}}
\int - \frac{1}{x^{8}} \, dx
1/(7*x**7)
polynomial
x
atom-0050
atomic
1
4*x**15
4 x^{15}
\int 4 x^{15} \, dx
x**16/4
polynomial
x
atom-0051
atomic
1
2*x**11
2 x^{11}
\int 2 x^{11} \, dx
x**12/6
polynomial
x
atom-0052
atomic
1
5*x**15
5 x^{15}
\int 5 x^{15} \, dx
5*x**16/16
polynomial
x
atom-0053
atomic
1
x**15
x^{15}
\int x^{15} \, dx
x**16/16
polynomial
x
atom-0054
atomic
1
3/x
\frac{3}{x}
\int \frac{3}{x} \, dx
3*log(x)
polynomial
x
atom-0055
atomic
1
-2/x**13
- \frac{2}{x^{13}}
\int - \frac{2}{x^{13}} \, dx
1/(6*x**12)
polynomial
x
atom-0056
atomic
1
4*x**2
4 x^{2}
\int 4 x^{2} \, dx
4*x**3/3
polynomial
x
atom-0057
atomic
1
-2/x**15
- \frac{2}{x^{15}}
\int - \frac{2}{x^{15}} \, dx
1/(7*x**14)
polynomial
x
atom-0058
atomic
1
5/x**14
\frac{5}{x^{14}}
\int \frac{5}{x^{14}} \, dx
-5/(13*x**13)
polynomial
x
atom-0059
atomic
1
-5*x**12
- 5 x^{12}
\int - 5 x^{12} \, dx
-5*x**13/13
polynomial
x
atom-0060
atomic
1
2/x**9
\frac{2}{x^{9}}
\int \frac{2}{x^{9}} \, dx
-1/(4*x**8)
polynomial
x
atom-0061
atomic
1
4*x**3
4 x^{3}
\int 4 x^{3} \, dx
x**4
polynomial
x
atom-0062
atomic
1
2*x**10
2 x^{10}
\int 2 x^{10} \, dx
2*x**11/11
polynomial
x
atom-0063
atomic
1
-4/x**12
- \frac{4}{x^{12}}
\int - \frac{4}{x^{12}} \, dx
4/(11*x**11)
polynomial
x
atom-0064
atomic
1
x**(-2)
\frac{1}{x^{2}}
\int \frac{1}{x^{2}} \, dx
-1/x
polynomial
x
atom-0065
atomic
1
5/x**12
\frac{5}{x^{12}}
\int \frac{5}{x^{12}} \, dx
-5/(11*x**11)
polynomial
x
atom-0066
atomic
1
-4/x**8
- \frac{4}{x^{8}}
\int - \frac{4}{x^{8}} \, dx
4/(7*x**7)
polynomial
x
atom-0067
atomic
1
-3/x**7
- \frac{3}{x^{7}}
\int - \frac{3}{x^{7}} \, dx
1/(2*x**6)
polynomial
x
atom-0068
atomic
1
-4/x
- \frac{4}{x}
\int - \frac{4}{x} \, dx
-4*log(x)
polynomial
x
atom-0069
atomic
1
3/x**12
\frac{3}{x^{12}}
\int \frac{3}{x^{12}} \, dx
-3/(11*x**11)
polynomial
x
atom-0070
atomic
1
3*x**11
3 x^{11}
\int 3 x^{11} \, dx
x**12/4
polynomial
x
atom-0071
atomic
1
-4*x**14
- 4 x^{14}
\int - 4 x^{14} \, dx
-4*x**15/15
polynomial
x
atom-0072
atomic
1
-5/x**10
- \frac{5}{x^{10}}
\int - \frac{5}{x^{10}} \, dx
5/(9*x**9)
polynomial
x
atom-0073
atomic
1
2/x**6
\frac{2}{x^{6}}
\int \frac{2}{x^{6}} \, dx
-2/(5*x**5)
polynomial
x
atom-0074
atomic
1
3*x**6
3 x^{6}
\int 3 x^{6} \, dx
3*x**7/7
polynomial
x
atom-0075
atomic
1
-3/x**9
- \frac{3}{x^{9}}
\int - \frac{3}{x^{9}} \, dx
3/(8*x**8)
polynomial
x
atom-0076
atomic
1
-5*x**3
- 5 x^{3}
\int - 5 x^{3} \, dx
-5*x**4/4
polynomial
x
atom-0077
atomic
1
3/x**10
\frac{3}{x^{10}}
\int \frac{3}{x^{10}} \, dx
-1/(3*x**9)
polynomial
x
atom-0078
atomic
1
3/x**13
\frac{3}{x^{13}}
\int \frac{3}{x^{13}} \, dx
-1/(4*x**12)
polynomial
x
atom-0079
atomic
1
-4*x**4
- 4 x^{4}
\int - 4 x^{4} \, dx
-4*x**5/5
polynomial
x
atom-0080
atomic
1
-2/x**3
- \frac{2}{x^{3}}
\int - \frac{2}{x^{3}} \, dx
x**(-2)
polynomial
x
atom-0081
atomic
1
4/x**8
\frac{4}{x^{8}}
\int \frac{4}{x^{8}} \, dx
-4/(7*x**7)
polynomial
x
atom-0082
atomic
1
-5*x**4
- 5 x^{4}
\int - 5 x^{4} \, dx
-x**5
polynomial
x
atom-0083
atomic
1
5*x**3
5 x^{3}
\int 5 x^{3} \, dx
5*x**4/4
polynomial
x
atom-0084
atomic
1
-1/x**9
- \frac{1}{x^{9}}
\int - \frac{1}{x^{9}} \, dx
1/(8*x**8)
polynomial
x
atom-0085
atomic
1
-2/x**7
- \frac{2}{x^{7}}
\int - \frac{2}{x^{7}} \, dx
1/(3*x**6)
polynomial
x
atom-0086
atomic
1
-4/x**15
- \frac{4}{x^{15}}
\int - \frac{4}{x^{15}} \, dx
2/(7*x**14)
polynomial
x
atom-0087
atomic
1
4/x**12
\frac{4}{x^{12}}
\int \frac{4}{x^{12}} \, dx
-4/(11*x**11)
polynomial
x
atom-0088
atomic
1
-2*x
- 2 x
\int - 2 x \, dx
-x**2
polynomial
x
atom-0089
atomic
1
-4*x**13
- 4 x^{13}
\int - 4 x^{13} \, dx
-2*x**14/7
polynomial
x
atom-0090
atomic
1
-1/x**10
- \frac{1}{x^{10}}
\int - \frac{1}{x^{10}} \, dx
1/(9*x**9)
polynomial
x
atom-0091
atomic
1
3*x**7
3 x^{7}
\int 3 x^{7} \, dx
3*x**8/8
polynomial
x
atom-0092
atomic
1
5*x
5 x
\int 5 x \, dx
5*x**2/2
polynomial
x
atom-0093
atomic
1
3/x**6
\frac{3}{x^{6}}
\int \frac{3}{x^{6}} \, dx
-3/(5*x**5)
polynomial
x
atom-0094
atomic
1
-4*x**15
- 4 x^{15}
\int - 4 x^{15} \, dx
-x**16/4
polynomial
x
atom-0095
atomic
1
-1/x**12
- \frac{1}{x^{12}}
\int - \frac{1}{x^{12}} \, dx
1/(11*x**11)
polynomial
x
atom-0096
atomic
1
3/x**11
\frac{3}{x^{11}}
\int \frac{3}{x^{11}} \, dx
-3/(10*x**10)
polynomial
x
atom-0097
atomic
1
-1/x**14
- \frac{1}{x^{14}}
\int - \frac{1}{x^{14}} \, dx
1/(13*x**13)
polynomial
x
atom-0098
atomic
1
-3*x**5
- 3 x^{5}
\int - 3 x^{5} \, dx
-x**6/2
polynomial
x
atom-0099
atomic
1
-3*x**8
- 3 x^{8}
\int - 3 x^{8} \, dx
-x**9/3
polynomial
x