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-0900
atomic
1
-5*x*exp(6 - 15*x)
- 5 x e^{6 - 15 x}
\int - 5 x e^{6 - 15 x} \, dx
(15*x + 1)*exp(6 - 15*x)/45
integration_primitive
x
atom-0901
atomic
1
4*x*sin(6*x)
4 x \sin{\left(6 x \right)}
\int 4 x \sin{\left(6 x \right)} \, dx
-2*x*cos(6*x)/3 + sin(6*x)/9
integration_primitive
x
atom-0902
atomic
1
3*x*exp(8 - 13*x)
3 x e^{8 - 13 x}
\int 3 x e^{8 - 13 x} \, dx
(-39*x - 3)*exp(8 - 13*x)/169
integration_primitive
x
atom-0903
atomic
1
5*x*cos(8*x + 1)
5 x \cos{\left(8 x + 1 \right)}
\int 5 x \cos{\left(8 x + 1 \right)} \, dx
5*x*sin(8*x + 1)/8 + 5*cos(8*x + 1)/64
integration_primitive
x
atom-0904
atomic
1
5*x*sin(12*x - 11)
5 x \sin{\left(12 x - 11 \right)}
\int 5 x \sin{\left(12 x - 11 \right)} \, dx
-5*x*cos(12*x - 11)/12 + 5*sin(12*x - 11)/144
integration_primitive
x
atom-0905
atomic
1
-x*cos(4*x - 10)
- x \cos{\left(4 x - 10 \right)}
\int - x \cos{\left(4 x - 10 \right)} \, dx
-x*sin(4*x - 10)/4 - cos(4*x - 10)/16
integration_primitive
x
atom-0906
atomic
1
-4*x*exp(12 - 12*x)
- 4 x e^{12 - 12 x}
\int - 4 x e^{12 - 12 x} \, dx
(12*x + 1)*exp(12 - 12*x)/36
integration_primitive
x
atom-0907
atomic
1
-3*x*sin(6*x + 5)
- 3 x \sin{\left(6 x + 5 \right)}
\int - 3 x \sin{\left(6 x + 5 \right)} \, dx
x*cos(6*x + 5)/2 - sin(6*x + 5)/12
integration_primitive
x
atom-0908
atomic
1
2*x*cos(15*x + 4)
2 x \cos{\left(15 x + 4 \right)}
\int 2 x \cos{\left(15 x + 4 \right)} \, dx
2*x*sin(15*x + 4)/15 + 2*cos(15*x + 4)/225
integration_primitive
x
atom-0909
atomic
1
-4*x*cos(4*x - 11)
- 4 x \cos{\left(4 x - 11 \right)}
\int - 4 x \cos{\left(4 x - 11 \right)} \, dx
-x*sin(4*x - 11) - cos(4*x - 11)/4
integration_primitive
x
atom-0910
atomic
1
x*log(15 - 3*x)
x \log{\left(15 - 3 x \right)}
\int x \log{\left(15 - 3 x \right)} \, dx
x**2*log(15 - 3*x)/2 - x**2/4 - 5*x/2 - 25*log(x - 5)/2
integration_primitive
x
atom-0911
atomic
1
x*log(7*x + 12)
x \log{\left(7 x + 12 \right)}
\int x \log{\left(7 x + 12 \right)} \, dx
x**2*log(7*x + 12)/2 - x**2/4 + 6*x/7 - 72*log(7*x + 12)/49
integration_primitive
x
atom-0912
atomic
1
5*x*sin(13*x + 10)
5 x \sin{\left(13 x + 10 \right)}
\int 5 x \sin{\left(13 x + 10 \right)} \, dx
-5*x*cos(13*x + 10)/13 + 5*sin(13*x + 10)/169
integration_primitive
x
atom-0913
atomic
1
-5*x*sin(15*x + 12)
- 5 x \sin{\left(15 x + 12 \right)}
\int - 5 x \sin{\left(15 x + 12 \right)} \, dx
x*cos(15*x + 12)/3 - sin(15*x + 12)/45
integration_primitive
x
atom-0914
atomic
1
4*x*log(10*x + 3)
4 x \log{\left(10 x + 3 \right)}
\int 4 x \log{\left(10 x + 3 \right)} \, dx
2*x**2*log(10*x + 3) - x**2 + 3*x/5 - 9*log(10*x + 3)/50
integration_primitive
x
atom-0915
atomic
1
x*atan(9*x - 4)
x \operatorname{atan}{\left(9 x - 4 \right)}
\int x \operatorname{atan}{\left(9 x - 4 \right)} \, dx
x**2*atan(9*x - 4)/2 - x/18 - 2*log(81*x**2 - 72*x + 17)/81 - 5*atan(9*x - 4)/54
integration_primitive
x
atom-0916
atomic
1
5*x*sin(13*x + 11)
5 x \sin{\left(13 x + 11 \right)}
\int 5 x \sin{\left(13 x + 11 \right)} \, dx
-5*x*cos(13*x + 11)/13 + 5*sin(13*x + 11)/169
integration_primitive
x
atom-0917
atomic
1
2*x*log(13 - 12*x)
2 x \log{\left(13 - 12 x \right)}
\int 2 x \log{\left(13 - 12 x \right)} \, dx
x**2*log(13 - 12*x) - x**2/2 - 13*x/12 - 169*log(12*x - 13)/144
integration_primitive
x
atom-0918
atomic
1
-4*x*cos(7*x - 5)
- 4 x \cos{\left(7 x - 5 \right)}
\int - 4 x \cos{\left(7 x - 5 \right)} \, dx
-4*x*sin(7*x - 5)/7 - 4*cos(7*x - 5)/49
integration_primitive
x
atom-0919
atomic
1
5*x*atan(x + 9)
5 x \operatorname{atan}{\left(x + 9 \right)}
\int 5 x \operatorname{atan}{\left(x + 9 \right)} \, dx
5*x**2*atan(x + 9)/2 - 5*x/2 + 45*log(x**2 + 18*x + 82)/2 - 200*atan(x + 9)
integration_primitive
x
atom-0920
atomic
1
-2*x*cos(15*x + 6)
- 2 x \cos{\left(15 x + 6 \right)}
\int - 2 x \cos{\left(15 x + 6 \right)} \, dx
-2*x*sin(15*x + 6)/15 - 2*cos(15*x + 6)/225
integration_primitive
x
atom-0921
atomic
1
-4*x*sin(12*x + 2)
- 4 x \sin{\left(12 x + 2 \right)}
\int - 4 x \sin{\left(12 x + 2 \right)} \, dx
x*cos(12*x + 2)/3 - sin(12*x + 2)/36
integration_primitive
x
atom-0922
atomic
1
5*x*log(6*x + 5)
5 x \log{\left(6 x + 5 \right)}
\int 5 x \log{\left(6 x + 5 \right)} \, dx
5*x**2*log(6*x + 5)/2 - 5*x**2/4 + 25*x/12 - 125*log(6*x + 5)/72
integration_primitive
x
atom-0923
atomic
1
3*x*exp(13*x + 4)
3 x e^{13 x + 4}
\int 3 x e^{13 x + 4} \, dx
(39*x - 3)*exp(13*x + 4)/169
integration_primitive
x
atom-0924
atomic
1
-3*x*log(x + 12)
- 3 x \log{\left(x + 12 \right)}
\int - 3 x \log{\left(x + 12 \right)} \, dx
-3*x**2*log(x + 12)/2 + 3*x**2/4 - 18*x + 216*log(x + 12)
integration_primitive
x
atom-0925
atomic
1
-3*x*log(9 - 13*x)
- 3 x \log{\left(9 - 13 x \right)}
\int - 3 x \log{\left(9 - 13 x \right)} \, dx
-3*x**2*log(9 - 13*x)/2 + 3*x**2/4 + 27*x/26 + 243*log(13*x - 9)/338
integration_primitive
x
atom-0926
atomic
1
x*sin(14*x - 1)
x \sin{\left(14 x - 1 \right)}
\int x \sin{\left(14 x - 1 \right)} \, dx
-x*cos(14*x - 1)/14 + sin(14*x - 1)/196
integration_primitive
x
atom-0927
atomic
1
-x*sin(3*x - 11)
- x \sin{\left(3 x - 11 \right)}
\int - x \sin{\left(3 x - 11 \right)} \, dx
x*cos(3*x - 11)/3 - sin(3*x - 11)/9
integration_primitive
x
atom-0928
atomic
1
2*x*log(10*x + 3)
2 x \log{\left(10 x + 3 \right)}
\int 2 x \log{\left(10 x + 3 \right)} \, dx
x**2*log(10*x + 3) - x**2/2 + 3*x/10 - 9*log(10*x + 3)/100
integration_primitive
x
atom-0929
atomic
1
2*x*exp(-x - 5)
2 x e^{- x - 5}
\int 2 x e^{- x - 5} \, dx
(-2*x - 2)*exp(-x - 5)
integration_primitive
x
atom-0930
atomic
1
5*x*log(-15*x - 12)
5 x \log{\left(- 15 x - 12 \right)}
\int 5 x \log{\left(- 15 x - 12 \right)} \, dx
5*x**2*log(-15*x - 12)/2 - 5*x**2/4 + 2*x - 8*log(5*x + 4)/5
integration_primitive
x
atom-0931
atomic
1
3*x*exp(2*x - 15)
3 x e^{2 x - 15}
\int 3 x e^{2 x - 15} \, dx
(6*x - 3)*exp(2*x - 15)/4
integration_primitive
x
atom-0932
atomic
1
4*x*atan(5*x - 6)
4 x \operatorname{atan}{\left(5 x - 6 \right)}
\int 4 x \operatorname{atan}{\left(5 x - 6 \right)} \, dx
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
integration_primitive
x
atom-0933
atomic
1
5*x*cos(6*x - 1)
5 x \cos{\left(6 x - 1 \right)}
\int 5 x \cos{\left(6 x - 1 \right)} \, dx
5*x*sin(6*x - 1)/6 + 5*cos(6*x - 1)/36
integration_primitive
x
atom-0934
atomic
1
-5*x*log(11*x - 8)
- 5 x \log{\left(11 x - 8 \right)}
\int - 5 x \log{\left(11 x - 8 \right)} \, dx
-5*x**2*log(11*x - 8)/2 + 5*x**2/4 + 20*x/11 + 160*log(11*x - 8)/121
integration_primitive
x
atom-0935
atomic
1
4*x*cos(4*x)
4 x \cos{\left(4 x \right)}
\int 4 x \cos{\left(4 x \right)} \, dx
x*sin(4*x) + cos(4*x)/4
integration_primitive
x
atom-0936
atomic
1
4*x*sin(12*x - 9)
4 x \sin{\left(12 x - 9 \right)}
\int 4 x \sin{\left(12 x - 9 \right)} \, dx
-x*cos(12*x - 9)/3 + sin(12*x - 9)/36
integration_primitive
x
atom-0937
atomic
1
5*x*cos(15*x + 10)
5 x \cos{\left(15 x + 10 \right)}
\int 5 x \cos{\left(15 x + 10 \right)} \, dx
x*sin(15*x + 10)/3 + cos(15*x + 10)/45
integration_primitive
x
atom-0938
atomic
1
4*x*sin(14*x - 13)
4 x \sin{\left(14 x - 13 \right)}
\int 4 x \sin{\left(14 x - 13 \right)} \, dx
-2*x*cos(14*x - 13)/7 + sin(14*x - 13)/49
integration_primitive
x
atom-0939
atomic
1
-x*atan(12*x + 7)
- x \operatorname{atan}{\left(12 x + 7 \right)}
\int - x \operatorname{atan}{\left(12 x + 7 \right)} \, dx
-x**2*atan(12*x + 7)/2 + x/24 - 7*log(72*x**2 + 84*x + 25)/288 + atan(12*x + 7)/6
integration_primitive
x
atom-0940
atomic
1
-4*x*log(14*x + 12)
- 4 x \log{\left(14 x + 12 \right)}
\int - 4 x \log{\left(14 x + 12 \right)} \, dx
-2*x**2*log(14*x + 12) + x**2 - 12*x/7 + 72*log(7*x + 6)/49
integration_primitive
x
atom-0941
atomic
1
-2*x*exp(7*x - 5)
- 2 x e^{7 x - 5}
\int - 2 x e^{7 x - 5} \, dx
(2 - 14*x)*exp(7*x - 5)/49
integration_primitive
x
atom-0942
atomic
1
-5*x*atan(14*x + 5)
- 5 x \operatorname{atan}{\left(14 x + 5 \right)}
\int - 5 x \operatorname{atan}{\left(14 x + 5 \right)} \, dx
-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
integration_primitive
x
atom-0943
atomic
1
-2*x*atan(x - 6)
- 2 x \operatorname{atan}{\left(x - 6 \right)}
\int - 2 x \operatorname{atan}{\left(x - 6 \right)} \, dx
-x**2*atan(x - 6) + x + 6*log(x**2 - 12*x + 37) + 35*atan(x - 6)
integration_primitive
x
atom-0944
atomic
1
-3*x*exp(15*x)
- 3 x e^{15 x}
\int - 3 x e^{15 x} \, dx
(1 - 15*x)*exp(15*x)/75
integration_primitive
x
atom-0945
atomic
1
-5*x*log(2*x + 14)
- 5 x \log{\left(2 x + 14 \right)}
\int - 5 x \log{\left(2 x + 14 \right)} \, dx
-5*x**2*log(2*x + 14)/2 + 5*x**2/4 - 35*x/2 + 245*log(x + 7)/2
integration_primitive
x
atom-0946
atomic
1
2*x*sin(14*x + 1)
2 x \sin{\left(14 x + 1 \right)}
\int 2 x \sin{\left(14 x + 1 \right)} \, dx
-x*cos(14*x + 1)/7 + sin(14*x + 1)/98
integration_primitive
x
atom-0947
atomic
1
-3*x*sin(8*x + 11)
- 3 x \sin{\left(8 x + 11 \right)}
\int - 3 x \sin{\left(8 x + 11 \right)} \, dx
3*x*cos(8*x + 11)/8 - 3*sin(8*x + 11)/64
integration_primitive
x
atom-0948
atomic
1
5*x*cos(4*x + 4)
5 x \cos{\left(4 x + 4 \right)}
\int 5 x \cos{\left(4 x + 4 \right)} \, dx
5*x*sin(4*x + 4)/4 + 5*cos(4*x + 4)/16
integration_primitive
x
atom-0949
atomic
1
-x*sin(2*x - 4)
- x \sin{\left(2 x - 4 \right)}
\int - x \sin{\left(2 x - 4 \right)} \, dx
x*cos(2*x - 4)/2 - sin(2*x - 4)/4
integration_primitive
x
atom-0950
atomic
1
x*sin(x - 10)
x \sin{\left(x - 10 \right)}
\int x \sin{\left(x - 10 \right)} \, dx
-x*cos(x - 10) + sin(x - 10)
integration_primitive
x
atom-0951
atomic
1
4*x*atan(7*x + 13)
4 x \operatorname{atan}{\left(7 x + 13 \right)}
\int 4 x \operatorname{atan}{\left(7 x + 13 \right)} \, dx
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
integration_primitive
x
atom-0952
atomic
1
3*x*atan(12*x - 5)
3 x \operatorname{atan}{\left(12 x - 5 \right)}
\int 3 x \operatorname{atan}{\left(12 x - 5 \right)} \, dx
3*x**2*atan(12*x - 5)/2 - x/8 - 5*log(72*x**2 - 60*x + 13)/96 - atan(12*x - 5)/4
integration_primitive
x
atom-0953
atomic
1
-2*x*cos(9*x - 4)
- 2 x \cos{\left(9 x - 4 \right)}
\int - 2 x \cos{\left(9 x - 4 \right)} \, dx
-2*x*sin(9*x - 4)/9 - 2*cos(9*x - 4)/81
integration_primitive
x
atom-0954
atomic
1
-5*x*sin(11*x - 7)
- 5 x \sin{\left(11 x - 7 \right)}
\int - 5 x \sin{\left(11 x - 7 \right)} \, dx
5*x*cos(11*x - 7)/11 - 5*sin(11*x - 7)/121
integration_primitive
x
atom-0955
atomic
1
5*x*exp(7 - 5*x)
5 x e^{7 - 5 x}
\int 5 x e^{7 - 5 x} \, dx
(-5*x - 1)*exp(7 - 5*x)/5
integration_primitive
x
atom-0956
atomic
1
3*x*log(3*x + 3)
3 x \log{\left(3 x + 3 \right)}
\int 3 x \log{\left(3 x + 3 \right)} \, dx
3*x**2*log(3*x + 3)/2 - 3*x**2/4 + 3*x/2 - 3*log(x + 1)/2
integration_primitive
x
atom-0957
atomic
1
3*x*log(13 - 6*x)
3 x \log{\left(13 - 6 x \right)}
\int 3 x \log{\left(13 - 6 x \right)} \, dx
3*x**2*log(13 - 6*x)/2 - 3*x**2/4 - 13*x/4 - 169*log(6*x - 13)/24
integration_primitive
x
atom-0958
atomic
1
3*x*log(-12*x - 15)
3 x \log{\left(- 12 x - 15 \right)}
\int 3 x \log{\left(- 12 x - 15 \right)} \, dx
3*x**2*log(-12*x - 15)/2 - 3*x**2/4 + 15*x/8 - 75*log(4*x + 5)/32
integration_primitive
x
atom-0959
atomic
1
5*x*cos(14*x + 9)
5 x \cos{\left(14 x + 9 \right)}
\int 5 x \cos{\left(14 x + 9 \right)} \, dx
5*x*sin(14*x + 9)/14 + 5*cos(14*x + 9)/196
integration_primitive
x
atom-0960
atomic
1
-3*x*cos(6*x - 6)
- 3 x \cos{\left(6 x - 6 \right)}
\int - 3 x \cos{\left(6 x - 6 \right)} \, dx
-x*sin(6*x - 6)/2 - cos(6*x - 6)/12
integration_primitive
x
atom-0961
atomic
1
-5*x*cos(7*x + 10)
- 5 x \cos{\left(7 x + 10 \right)}
\int - 5 x \cos{\left(7 x + 10 \right)} \, dx
-5*x*sin(7*x + 10)/7 - 5*cos(7*x + 10)/49
integration_primitive
x
atom-0962
atomic
1
3*x*log(-14*x - 4)
3 x \log{\left(- 14 x - 4 \right)}
\int 3 x \log{\left(- 14 x - 4 \right)} \, dx
3*x**2*log(-14*x - 4)/2 - 3*x**2/4 + 3*x/7 - 6*log(7*x + 2)/49
integration_primitive
x
atom-0963
atomic
1
5*x*sin(8*x + 2)
5 x \sin{\left(8 x + 2 \right)}
\int 5 x \sin{\left(8 x + 2 \right)} \, dx
-5*x*cos(8*x + 2)/8 + 5*sin(8*x + 2)/64
integration_primitive
x
atom-0964
atomic
1
-3*x*atan(3*x + 8)
- 3 x \operatorname{atan}{\left(3 x + 8 \right)}
\int - 3 x \operatorname{atan}{\left(3 x + 8 \right)} \, dx
-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
integration_primitive
x
atom-0965
atomic
1
-x*exp(7*x + 6)
- x e^{7 x + 6}
\int - x e^{7 x + 6} \, dx
(1 - 7*x)*exp(7*x + 6)/49
integration_primitive
x
atom-0966
atomic
1
x*cos(2*x - 15)
x \cos{\left(2 x - 15 \right)}
\int x \cos{\left(2 x - 15 \right)} \, dx
x*sin(2*x - 15)/2 + cos(2*x - 15)/4
integration_primitive
x
atom-0967
atomic
1
-5*x*cos(15*x - 8)
- 5 x \cos{\left(15 x - 8 \right)}
\int - 5 x \cos{\left(15 x - 8 \right)} \, dx
-x*sin(15*x - 8)/3 - cos(15*x - 8)/45
integration_primitive
x
atom-0968
atomic
1
3*x*sin(8*x + 4)
3 x \sin{\left(8 x + 4 \right)}
\int 3 x \sin{\left(8 x + 4 \right)} \, dx
-3*x*cos(8*x + 4)/8 + 3*sin(8*x + 4)/64
integration_primitive
x
atom-0969
atomic
1
2*x*sin(6*x + 1)
2 x \sin{\left(6 x + 1 \right)}
\int 2 x \sin{\left(6 x + 1 \right)} \, dx
-x*cos(6*x + 1)/3 + sin(6*x + 1)/18
integration_primitive
x
atom-0970
atomic
1
-4*x*log(-3*x - 14)
- 4 x \log{\left(- 3 x - 14 \right)}
\int - 4 x \log{\left(- 3 x - 14 \right)} \, dx
-2*x**2*log(-3*x - 14) + x**2 - 28*x/3 + 392*log(3*x + 14)/9
integration_primitive
x
atom-0971
atomic
1
x*atan(11*x + 10)
x \operatorname{atan}{\left(11 x + 10 \right)}
\int x \operatorname{atan}{\left(11 x + 10 \right)} \, dx
x**2*atan(11*x + 10)/2 - x/22 + 5*log(121*x**2 + 220*x + 101)/121 - 9*atan(11*x + 10)/22
integration_primitive
x
atom-0972
atomic
1
5*x*sin(5*x + 1)
5 x \sin{\left(5 x + 1 \right)}
\int 5 x \sin{\left(5 x + 1 \right)} \, dx
-x*cos(5*x + 1) + sin(5*x + 1)/5
integration_primitive
x
atom-0973
atomic
1
-4*x*atan(14*x - 9)
- 4 x \operatorname{atan}{\left(14 x - 9 \right)}
\int - 4 x \operatorname{atan}{\left(14 x - 9 \right)} \, dx
-2*x**2*atan(14*x - 9) + x/7 + 9*log(98*x**2 - 126*x + 41)/98 + 40*atan(14*x - 9)/49
integration_primitive
x
atom-0974
atomic
1
-x*atan(10*x + 3)
- x \operatorname{atan}{\left(10 x + 3 \right)}
\int - x \operatorname{atan}{\left(10 x + 3 \right)} \, dx
-x**2*atan(10*x + 3)/2 + x/20 - 3*log(10*x**2 + 6*x + 1)/200 + atan(10*x + 3)/25
integration_primitive
x
atom-0975
atomic
1
-3*x*sin(8*x - 15)
- 3 x \sin{\left(8 x - 15 \right)}
\int - 3 x \sin{\left(8 x - 15 \right)} \, dx
3*x*cos(8*x - 15)/8 - 3*sin(8*x - 15)/64
integration_primitive
x
atom-0976
atomic
1
-3*x*atan(10*x + 2)
- 3 x \operatorname{atan}{\left(10 x + 2 \right)}
\int - 3 x \operatorname{atan}{\left(10 x + 2 \right)} \, dx
-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
integration_primitive
x
atom-0977
atomic
1
4*x*sin(4*x + 8)
4 x \sin{\left(4 x + 8 \right)}
\int 4 x \sin{\left(4 x + 8 \right)} \, dx
-x*cos(4*x + 8) + sin(4*x + 8)/4
integration_primitive
x
atom-0978
atomic
1
x*atan(9*x - 15)
x \operatorname{atan}{\left(9 x - 15 \right)}
\int x \operatorname{atan}{\left(9 x - 15 \right)} \, dx
x**2*atan(9*x - 15)/2 - x/18 - 5*log(81*x**2 - 270*x + 226)/54 - 112*atan(9*x - 15)/81
integration_primitive
x
atom-0979
atomic
1
3*x*exp(11*x + 9)
3 x e^{11 x + 9}
\int 3 x e^{11 x + 9} \, dx
(33*x - 3)*exp(11*x + 9)/121
integration_primitive
x
atom-0980
atomic
1
-2*x*atan(8*x - 13)
- 2 x \operatorname{atan}{\left(8 x - 13 \right)}
\int - 2 x \operatorname{atan}{\left(8 x - 13 \right)} \, dx
-x**2*atan(8*x - 13) + x/8 + 13*log(32*x**2 - 104*x + 85)/64 + 21*atan(8*x - 13)/8
integration_primitive
x
atom-0981
atomic
1
-2*x*cos(15*x - 14)
- 2 x \cos{\left(15 x - 14 \right)}
\int - 2 x \cos{\left(15 x - 14 \right)} \, dx
-2*x*sin(15*x - 14)/15 - 2*cos(15*x - 14)/225
integration_primitive
x
atom-0982
atomic
1
4*x*atan(3*x + 7)
4 x \operatorname{atan}{\left(3 x + 7 \right)}
\int 4 x \operatorname{atan}{\left(3 x + 7 \right)} \, dx
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
integration_primitive
x
atom-0983
atomic
1
-5*x*cos(14*x + 1)
- 5 x \cos{\left(14 x + 1 \right)}
\int - 5 x \cos{\left(14 x + 1 \right)} \, dx
-5*x*sin(14*x + 1)/14 - 5*cos(14*x + 1)/196
integration_primitive
x
atom-0984
atomic
1
3*x*exp(-x)
3 x e^{- x}
\int 3 x e^{- x} \, dx
(-3*x - 3)*exp(-x)
integration_primitive
x
atom-0985
atomic
1
-5*x*atan(9*x + 5)
- 5 x \operatorname{atan}{\left(9 x + 5 \right)}
\int - 5 x \operatorname{atan}{\left(9 x + 5 \right)} \, dx
-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
integration_primitive
x
atom-0986
atomic
1
4*x*atan(10*x - 15)
4 x \operatorname{atan}{\left(10 x - 15 \right)}
\int 4 x \operatorname{atan}{\left(10 x - 15 \right)} \, dx
2*x**2*atan(10*x - 15) - x/5 - 3*log(50*x**2 - 150*x + 113)/10 - 112*atan(10*x - 15)/25
integration_primitive
x
atom-0987
atomic
1
-5*x*sin(13*x + 9)
- 5 x \sin{\left(13 x + 9 \right)}
\int - 5 x \sin{\left(13 x + 9 \right)} \, dx
5*x*cos(13*x + 9)/13 - 5*sin(13*x + 9)/169
integration_primitive
x
atom-0988
atomic
1
x*sin(11*x - 12)
x \sin{\left(11 x - 12 \right)}
\int x \sin{\left(11 x - 12 \right)} \, dx
-x*cos(11*x - 12)/11 + sin(11*x - 12)/121
integration_primitive
x
atom-0989
atomic
1
x*exp(5*x + 11)
x e^{5 x + 11}
\int x e^{5 x + 11} \, dx
(5*x - 1)*exp(5*x + 11)/25
integration_primitive
x
atom-0990
atomic
1
-3*x*cos(15*x + 1)
- 3 x \cos{\left(15 x + 1 \right)}
\int - 3 x \cos{\left(15 x + 1 \right)} \, dx
-x*sin(15*x + 1)/5 - cos(15*x + 1)/75
integration_primitive
x
atom-0991
atomic
1
-4*x*cos(14*x + 10)
- 4 x \cos{\left(14 x + 10 \right)}
\int - 4 x \cos{\left(14 x + 10 \right)} \, dx
-2*x*sin(14*x + 10)/7 - cos(14*x + 10)/49
integration_primitive
x
atom-0992
atomic
1
4*x*cos(11*x - 8)
4 x \cos{\left(11 x - 8 \right)}
\int 4 x \cos{\left(11 x - 8 \right)} \, dx
4*x*sin(11*x - 8)/11 + 4*cos(11*x - 8)/121
integration_primitive
x
atom-0993
atomic
1
2*x*log(5*x - 3)
2 x \log{\left(5 x - 3 \right)}
\int 2 x \log{\left(5 x - 3 \right)} \, dx
x**2*log(5*x - 3) - x**2/2 - 3*x/5 - 9*log(5*x - 3)/25
integration_primitive
x
atom-0994
atomic
1
x*atan(6*x - 12)
x \operatorname{atan}{\left(6 x - 12 \right)}
\int x \operatorname{atan}{\left(6 x - 12 \right)} \, dx
x**2*atan(6*x - 12)/2 - x/12 - log(36*x**2 - 144*x + 145)/6 - 143*atan(6*x - 12)/72
integration_primitive
x
atom-0995
atomic
1
-4*x*atan(13*x - 9)
- 4 x \operatorname{atan}{\left(13 x - 9 \right)}
\int - 4 x \operatorname{atan}{\left(13 x - 9 \right)} \, dx
-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
integration_primitive
x
atom-0996
atomic
1
4*x*atan(4*x - 14)
4 x \operatorname{atan}{\left(4 x - 14 \right)}
\int 4 x \operatorname{atan}{\left(4 x - 14 \right)} \, dx
2*x**2*atan(4*x - 14) - x/2 - 7*log(16*x**2 - 112*x + 197)/4 - 195*atan(4*x - 14)/8
integration_primitive
x
atom-0997
atomic
1
5*x*exp(4 - 6*x)
5 x e^{4 - 6 x}
\int 5 x e^{4 - 6 x} \, dx
(-30*x - 5)*exp(4 - 6*x)/36
integration_primitive
x
atom-0998
atomic
1
2*x*exp(-3*x - 3)
2 x e^{- 3 x - 3}
\int 2 x e^{- 3 x - 3} \, dx
(-6*x - 2)*exp(-3*x - 3)/9
integration_primitive
x
atom-0999
atomic
1
3*x*log(-8*x - 11)
3 x \log{\left(- 8 x - 11 \right)}
\int 3 x \log{\left(- 8 x - 11 \right)} \, dx
3*x**2*log(-8*x - 11)/2 - 3*x**2/4 + 33*x/16 - 363*log(8*x + 11)/128
integration_primitive
x