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-0800
atomic
1
4*x*sin(15*x + 9)
4 x \sin{\left(15 x + 9 \right)}
\int 4 x \sin{\left(15 x + 9 \right)} \, dx
-4*x*cos(15*x + 9)/15 + 4*sin(15*x + 9)/225
integration_primitive
x
atom-0801
atomic
1
-4*x*cos(12*x - 12)
- 4 x \cos{\left(12 x - 12 \right)}
\int - 4 x \cos{\left(12 x - 12 \right)} \, dx
-x*sin(12*x - 12)/3 - cos(12*x - 12)/36
integration_primitive
x
atom-0802
atomic
1
2*x*cos(13*x + 6)
2 x \cos{\left(13 x + 6 \right)}
\int 2 x \cos{\left(13 x + 6 \right)} \, dx
2*x*sin(13*x + 6)/13 + 2*cos(13*x + 6)/169
integration_primitive
x
atom-0803
atomic
1
3*x*cos(3*x + 10)
3 x \cos{\left(3 x + 10 \right)}
\int 3 x \cos{\left(3 x + 10 \right)} \, dx
x*sin(3*x + 10) + cos(3*x + 10)/3
integration_primitive
x
atom-0804
atomic
1
-3*x*cos(x + 14)
- 3 x \cos{\left(x + 14 \right)}
\int - 3 x \cos{\left(x + 14 \right)} \, dx
-3*x*sin(x + 14) - 3*cos(x + 14)
integration_primitive
x
atom-0805
atomic
1
-x*cos(8*x - 11)
- x \cos{\left(8 x - 11 \right)}
\int - x \cos{\left(8 x - 11 \right)} \, dx
-x*sin(8*x - 11)/8 - cos(8*x - 11)/64
integration_primitive
x
atom-0806
atomic
1
-3*x*exp(9*x + 7)
- 3 x e^{9 x + 7}
\int - 3 x e^{9 x + 7} \, dx
(1 - 9*x)*exp(9*x + 7)/27
integration_primitive
x
atom-0807
atomic
1
-3*x*atan(2*x - 9)
- 3 x \operatorname{atan}{\left(2 x - 9 \right)}
\int - 3 x \operatorname{atan}{\left(2 x - 9 \right)} \, dx
-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)
integration_primitive
x
atom-0808
atomic
1
-5*x*atan(11*x - 3)
- 5 x \operatorname{atan}{\left(11 x - 3 \right)}
\int - 5 x \operatorname{atan}{\left(11 x - 3 \right)} \, dx
-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
integration_primitive
x
atom-0809
atomic
1
3*x*log(6*x + 12)
3 x \log{\left(6 x + 12 \right)}
\int 3 x \log{\left(6 x + 12 \right)} \, dx
3*x**2*log(6*x + 12)/2 - 3*x**2/4 + 3*x - 6*log(x + 2)
integration_primitive
x
atom-0810
atomic
1
-2*x*log(-6*x - 13)
- 2 x \log{\left(- 6 x - 13 \right)}
\int - 2 x \log{\left(- 6 x - 13 \right)} \, dx
-x**2*log(-6*x - 13) + x**2/2 - 13*x/6 + 169*log(6*x + 13)/36
integration_primitive
x
atom-0811
atomic
1
-5*x*atan(x + 3)
- 5 x \operatorname{atan}{\left(x + 3 \right)}
\int - 5 x \operatorname{atan}{\left(x + 3 \right)} \, dx
-5*x**2*atan(x + 3)/2 + 5*x/2 - 15*log(x**2 + 6*x + 10)/2 + 20*atan(x + 3)
integration_primitive
x
atom-0812
atomic
1
5*x*exp(4*x - 11)
5 x e^{4 x - 11}
\int 5 x e^{4 x - 11} \, dx
(20*x - 5)*exp(4*x - 11)/16
integration_primitive
x
atom-0813
atomic
1
-2*x*sin(10*x - 15)
- 2 x \sin{\left(10 x - 15 \right)}
\int - 2 x \sin{\left(10 x - 15 \right)} \, dx
x*cos(10*x - 15)/5 - sin(10*x - 15)/50
integration_primitive
x
atom-0814
atomic
1
-2*x*log(-11*x - 14)
- 2 x \log{\left(- 11 x - 14 \right)}
\int - 2 x \log{\left(- 11 x - 14 \right)} \, dx
-x**2*log(-11*x - 14) + x**2/2 - 14*x/11 + 196*log(11*x + 14)/121
integration_primitive
x
atom-0815
atomic
1
-5*x*sin(2*x + 9)
- 5 x \sin{\left(2 x + 9 \right)}
\int - 5 x \sin{\left(2 x + 9 \right)} \, dx
5*x*cos(2*x + 9)/2 - 5*sin(2*x + 9)/4
integration_primitive
x
atom-0816
atomic
1
-x*exp(14 - 5*x)
- x e^{14 - 5 x}
\int - x e^{14 - 5 x} \, dx
(5*x + 1)*exp(14 - 5*x)/25
integration_primitive
x
atom-0817
atomic
1
3*x*cos(3*x - 2)
3 x \cos{\left(3 x - 2 \right)}
\int 3 x \cos{\left(3 x - 2 \right)} \, dx
x*sin(3*x - 2) + cos(3*x - 2)/3
integration_primitive
x
atom-0818
atomic
1
3*x*exp(14 - x)
3 x e^{14 - x}
\int 3 x e^{14 - x} \, dx
(-3*x - 3)*exp(14 - x)
integration_primitive
x
atom-0819
atomic
1
4*x*log(3*x + 1)
4 x \log{\left(3 x + 1 \right)}
\int 4 x \log{\left(3 x + 1 \right)} \, dx
2*x**2*log(3*x + 1) - x**2 + 2*x/3 - 2*log(3*x + 1)/9
integration_primitive
x
atom-0820
atomic
1
3*x*atan(11*x - 3)
3 x \operatorname{atan}{\left(11 x - 3 \right)}
\int 3 x \operatorname{atan}{\left(11 x - 3 \right)} \, dx
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
integration_primitive
x
atom-0821
atomic
1
-4*x*atan(14*x - 12)
- 4 x \operatorname{atan}{\left(14 x - 12 \right)}
\int - 4 x \operatorname{atan}{\left(14 x - 12 \right)} \, dx
-2*x**2*atan(14*x - 12) + x/7 + 6*log(196*x**2 - 336*x + 145)/49 + 143*atan(14*x - 12)/98
integration_primitive
x
atom-0822
atomic
1
-x*cos(12*x + 2)
- x \cos{\left(12 x + 2 \right)}
\int - x \cos{\left(12 x + 2 \right)} \, dx
-x*sin(12*x + 2)/12 - cos(12*x + 2)/144
integration_primitive
x
atom-0823
atomic
1
-x*log(5 - 3*x)
- x \log{\left(5 - 3 x \right)}
\int - x \log{\left(5 - 3 x \right)} \, dx
-x**2*log(5 - 3*x)/2 + x**2/4 + 5*x/6 + 25*log(3*x - 5)/18
integration_primitive
x
atom-0824
atomic
1
2*x*cos(14*x + 10)
2 x \cos{\left(14 x + 10 \right)}
\int 2 x \cos{\left(14 x + 10 \right)} \, dx
x*sin(14*x + 10)/7 + cos(14*x + 10)/98
integration_primitive
x
atom-0825
atomic
1
4*x*log(4*x + 6)
4 x \log{\left(4 x + 6 \right)}
\int 4 x \log{\left(4 x + 6 \right)} \, dx
2*x**2*log(4*x + 6) - x**2 + 3*x - 9*log(2*x + 3)/2
integration_primitive
x
atom-0826
atomic
1
-2*x*log(8 - 14*x)
- 2 x \log{\left(8 - 14 x \right)}
\int - 2 x \log{\left(8 - 14 x \right)} \, dx
-x**2*log(8 - 14*x) + x**2/2 + 4*x/7 + 16*log(7*x - 4)/49
integration_primitive
x
atom-0827
atomic
1
-5*x*cos(5*x - 11)
- 5 x \cos{\left(5 x - 11 \right)}
\int - 5 x \cos{\left(5 x - 11 \right)} \, dx
-x*sin(5*x - 11) - cos(5*x - 11)/5
integration_primitive
x
atom-0828
atomic
1
2*x*exp(12*x + 7)
2 x e^{12 x + 7}
\int 2 x e^{12 x + 7} \, dx
(12*x - 1)*exp(12*x + 7)/72
integration_primitive
x
atom-0829
atomic
1
-2*x*log(-11*x - 6)
- 2 x \log{\left(- 11 x - 6 \right)}
\int - 2 x \log{\left(- 11 x - 6 \right)} \, dx
-x**2*log(-11*x - 6) + x**2/2 - 6*x/11 + 36*log(11*x + 6)/121
integration_primitive
x
atom-0830
atomic
1
-x*atan(8*x - 2)
- x \operatorname{atan}{\left(8 x - 2 \right)}
\int - x \operatorname{atan}{\left(8 x - 2 \right)} \, dx
-x**2*atan(8*x - 2)/2 + x/16 + log(64*x**2 - 32*x + 5)/64 + 3*atan(8*x - 2)/128
integration_primitive
x
atom-0831
atomic
1
-2*x*log(-x - 9)
- 2 x \log{\left(- x - 9 \right)}
\int - 2 x \log{\left(- x - 9 \right)} \, dx
-x**2*log(-x - 9) + x**2/2 - 9*x + 81*log(x + 9)
integration_primitive
x
atom-0832
atomic
1
3*x*exp(12*x - 4)
3 x e^{12 x - 4}
\int 3 x e^{12 x - 4} \, dx
(12*x - 1)*exp(12*x - 4)/48
integration_primitive
x
atom-0833
atomic
1
3*x*atan(13*x + 6)
3 x \operatorname{atan}{\left(13 x + 6 \right)}
\int 3 x \operatorname{atan}{\left(13 x + 6 \right)} \, dx
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
integration_primitive
x
atom-0834
atomic
1
3*x*exp(13*x + 3)
3 x e^{13 x + 3}
\int 3 x e^{13 x + 3} \, dx
(39*x - 3)*exp(13*x + 3)/169
integration_primitive
x
atom-0835
atomic
1
-2*x*sin(11*x - 14)
- 2 x \sin{\left(11 x - 14 \right)}
\int - 2 x \sin{\left(11 x - 14 \right)} \, dx
2*x*cos(11*x - 14)/11 - 2*sin(11*x - 14)/121
integration_primitive
x
atom-0836
atomic
1
-5*x*sin(14*x - 4)
- 5 x \sin{\left(14 x - 4 \right)}
\int - 5 x \sin{\left(14 x - 4 \right)} \, dx
5*x*cos(14*x - 4)/14 - 5*sin(14*x - 4)/196
integration_primitive
x
atom-0837
atomic
1
2*x*exp(x - 3)
2 x e^{x - 3}
\int 2 x e^{x - 3} \, dx
(2*x - 2)*exp(x - 3)
integration_primitive
x
atom-0838
atomic
1
2*x*atan(4*x)
2 x \operatorname{atan}{\left(4 x \right)}
\int 2 x \operatorname{atan}{\left(4 x \right)} \, dx
x**2*atan(4*x) - x/4 + atan(4*x)/16
integration_primitive
x
atom-0839
atomic
1
2*x*cos(3*x + 2)
2 x \cos{\left(3 x + 2 \right)}
\int 2 x \cos{\left(3 x + 2 \right)} \, dx
2*x*sin(3*x + 2)/3 + 2*cos(3*x + 2)/9
integration_primitive
x
atom-0840
atomic
1
-x*exp(8*x + 11)
- x e^{8 x + 11}
\int - x e^{8 x + 11} \, dx
(1 - 8*x)*exp(8*x + 11)/64
integration_primitive
x
atom-0841
atomic
1
-x*atan(14*x + 10)
- x \operatorname{atan}{\left(14 x + 10 \right)}
\int - x \operatorname{atan}{\left(14 x + 10 \right)} \, dx
-x**2*atan(14*x + 10)/2 + x/28 - 5*log(196*x**2 + 280*x + 101)/196 + 99*atan(14*x + 10)/392
integration_primitive
x
atom-0842
atomic
1
-2*x*sin(12*x - 8)
- 2 x \sin{\left(12 x - 8 \right)}
\int - 2 x \sin{\left(12 x - 8 \right)} \, dx
x*cos(12*x - 8)/6 - sin(12*x - 8)/72
integration_primitive
x
atom-0843
atomic
1
-x*atan(5*x - 2)
- x \operatorname{atan}{\left(5 x - 2 \right)}
\int - x \operatorname{atan}{\left(5 x - 2 \right)} \, dx
-x**2*atan(5*x - 2)/2 + x/10 + log(5*x**2 - 4*x + 1)/25 + 3*atan(5*x - 2)/50
integration_primitive
x
atom-0844
atomic
1
-5*x*sin(15*x)
- 5 x \sin{\left(15 x \right)}
\int - 5 x \sin{\left(15 x \right)} \, dx
x*cos(15*x)/3 - sin(15*x)/45
integration_primitive
x
atom-0845
atomic
1
4*x*sin(10*x - 15)
4 x \sin{\left(10 x - 15 \right)}
\int 4 x \sin{\left(10 x - 15 \right)} \, dx
-2*x*cos(10*x - 15)/5 + sin(10*x - 15)/25
integration_primitive
x
atom-0846
atomic
1
-x*cos(7*x + 15)
- x \cos{\left(7 x + 15 \right)}
\int - x \cos{\left(7 x + 15 \right)} \, dx
-x*sin(7*x + 15)/7 - cos(7*x + 15)/49
integration_primitive
x
atom-0847
atomic
1
x*log(12*x - 4)
x \log{\left(12 x - 4 \right)}
\int x \log{\left(12 x - 4 \right)} \, dx
x**2*log(12*x - 4)/2 - x**2/4 - x/6 - log(3*x - 1)/18
integration_primitive
x
atom-0848
atomic
1
-2*x*atan(6*x - 6)
- 2 x \operatorname{atan}{\left(6 x - 6 \right)}
\int - 2 x \operatorname{atan}{\left(6 x - 6 \right)} \, dx
-x**2*atan(6*x - 6) + x/6 + log(36*x**2 - 72*x + 37)/6 + 35*atan(6*x - 6)/36
integration_primitive
x
atom-0849
atomic
1
x*exp(3*x - 12)
x e^{3 x - 12}
\int x e^{3 x - 12} \, dx
(3*x - 1)*exp(3*x - 12)/9
integration_primitive
x
atom-0850
atomic
1
5*x*cos(15*x + 11)
5 x \cos{\left(15 x + 11 \right)}
\int 5 x \cos{\left(15 x + 11 \right)} \, dx
x*sin(15*x + 11)/3 + cos(15*x + 11)/45
integration_primitive
x
atom-0851
atomic
1
4*x*cos(4*x - 6)
4 x \cos{\left(4 x - 6 \right)}
\int 4 x \cos{\left(4 x - 6 \right)} \, dx
x*sin(4*x - 6) + cos(4*x - 6)/4
integration_primitive
x
atom-0852
atomic
1
2*x*cos(13*x + 5)
2 x \cos{\left(13 x + 5 \right)}
\int 2 x \cos{\left(13 x + 5 \right)} \, dx
2*x*sin(13*x + 5)/13 + 2*cos(13*x + 5)/169
integration_primitive
x
atom-0853
atomic
1
-x*cos(7*x - 5)
- x \cos{\left(7 x - 5 \right)}
\int - x \cos{\left(7 x - 5 \right)} \, dx
-x*sin(7*x - 5)/7 - cos(7*x - 5)/49
integration_primitive
x
atom-0854
atomic
1
3*x*exp(9*x - 8)
3 x e^{9 x - 8}
\int 3 x e^{9 x - 8} \, dx
(9*x - 1)*exp(9*x - 8)/27
integration_primitive
x
atom-0855
atomic
1
4*x*cos(3*x - 6)
4 x \cos{\left(3 x - 6 \right)}
\int 4 x \cos{\left(3 x - 6 \right)} \, dx
4*x*sin(3*x - 6)/3 + 4*cos(3*x - 6)/9
integration_primitive
x
atom-0856
atomic
1
-5*x*cos(5*x)
- 5 x \cos{\left(5 x \right)}
\int - 5 x \cos{\left(5 x \right)} \, dx
-x*sin(5*x) - cos(5*x)/5
integration_primitive
x
atom-0857
atomic
1
x*exp(-3*x - 3)
x e^{- 3 x - 3}
\int x e^{- 3 x - 3} \, dx
(-3*x - 1)*exp(-3*x - 3)/9
integration_primitive
x
atom-0858
atomic
1
4*x*cos(11*x - 9)
4 x \cos{\left(11 x - 9 \right)}
\int 4 x \cos{\left(11 x - 9 \right)} \, dx
4*x*sin(11*x - 9)/11 + 4*cos(11*x - 9)/121
integration_primitive
x
atom-0859
atomic
1
-2*x*log(6*x + 2)
- 2 x \log{\left(6 x + 2 \right)}
\int - 2 x \log{\left(6 x + 2 \right)} \, dx
-x**2*log(6*x + 2) + x**2/2 - x/3 + log(3*x + 1)/9
integration_primitive
x
atom-0860
atomic
1
5*x*cos(4*x - 1)
5 x \cos{\left(4 x - 1 \right)}
\int 5 x \cos{\left(4 x - 1 \right)} \, dx
5*x*sin(4*x - 1)/4 + 5*cos(4*x - 1)/16
integration_primitive
x
atom-0861
atomic
1
5*x*sin(13*x + 2)
5 x \sin{\left(13 x + 2 \right)}
\int 5 x \sin{\left(13 x + 2 \right)} \, dx
-5*x*cos(13*x + 2)/13 + 5*sin(13*x + 2)/169
integration_primitive
x
atom-0862
atomic
1
2*x*cos(11*x - 8)
2 x \cos{\left(11 x - 8 \right)}
\int 2 x \cos{\left(11 x - 8 \right)} \, dx
2*x*sin(11*x - 8)/11 + 2*cos(11*x - 8)/121
integration_primitive
x
atom-0863
atomic
1
3*x*sin(9*x + 14)
3 x \sin{\left(9 x + 14 \right)}
\int 3 x \sin{\left(9 x + 14 \right)} \, dx
-x*cos(9*x + 14)/3 + sin(9*x + 14)/27
integration_primitive
x
atom-0864
atomic
1
5*x*cos(13*x + 8)
5 x \cos{\left(13 x + 8 \right)}
\int 5 x \cos{\left(13 x + 8 \right)} \, dx
5*x*sin(13*x + 8)/13 + 5*cos(13*x + 8)/169
integration_primitive
x
atom-0865
atomic
1
-x*cos(2*x - 10)
- x \cos{\left(2 x - 10 \right)}
\int - x \cos{\left(2 x - 10 \right)} \, dx
-x*sin(2*x - 10)/2 - cos(2*x - 10)/4
integration_primitive
x
atom-0866
atomic
1
4*x*exp(-6*x - 1)
4 x e^{- 6 x - 1}
\int 4 x e^{- 6 x - 1} \, dx
(-6*x - 1)*exp(-6*x - 1)/9
integration_primitive
x
atom-0867
atomic
1
5*x*atan(3*x + 3)
5 x \operatorname{atan}{\left(3 x + 3 \right)}
\int 5 x \operatorname{atan}{\left(3 x + 3 \right)} \, dx
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
integration_primitive
x
atom-0868
atomic
1
-2*x*log(x - 12)
- 2 x \log{\left(x - 12 \right)}
\int - 2 x \log{\left(x - 12 \right)} \, dx
-x**2*log(x - 12) + x**2/2 + 12*x + 144*log(x - 12)
integration_primitive
x
atom-0869
atomic
1
-x*sin(14*x - 12)
- x \sin{\left(14 x - 12 \right)}
\int - x \sin{\left(14 x - 12 \right)} \, dx
x*cos(14*x - 12)/14 - sin(14*x - 12)/196
integration_primitive
x
atom-0870
atomic
1
2*x*atan(5*x + 2)
2 x \operatorname{atan}{\left(5 x + 2 \right)}
\int 2 x \operatorname{atan}{\left(5 x + 2 \right)} \, dx
x**2*atan(5*x + 2) - x/5 + 2*log(5*x**2 + 4*x + 1)/25 - 3*atan(5*x + 2)/25
integration_primitive
x
atom-0871
atomic
1
-2*x*sin(11*x + 5)
- 2 x \sin{\left(11 x + 5 \right)}
\int - 2 x \sin{\left(11 x + 5 \right)} \, dx
2*x*cos(11*x + 5)/11 - 2*sin(11*x + 5)/121
integration_primitive
x
atom-0872
atomic
1
-2*x*sin(5*x - 5)
- 2 x \sin{\left(5 x - 5 \right)}
\int - 2 x \sin{\left(5 x - 5 \right)} \, dx
2*x*cos(5*x - 5)/5 - 2*sin(5*x - 5)/25
integration_primitive
x
atom-0873
atomic
1
-5*x*cos(15*x + 1)
- 5 x \cos{\left(15 x + 1 \right)}
\int - 5 x \cos{\left(15 x + 1 \right)} \, dx
-x*sin(15*x + 1)/3 - cos(15*x + 1)/45
integration_primitive
x
atom-0874
atomic
1
-3*x*sin(3*x + 9)
- 3 x \sin{\left(3 x + 9 \right)}
\int - 3 x \sin{\left(3 x + 9 \right)} \, dx
x*cos(3*x + 9) - sin(3*x + 9)/3
integration_primitive
x
atom-0875
atomic
1
-4*x*log(4 - 11*x)
- 4 x \log{\left(4 - 11 x \right)}
\int - 4 x \log{\left(4 - 11 x \right)} \, dx
-2*x**2*log(4 - 11*x) + x**2 + 8*x/11 + 32*log(11*x - 4)/121
integration_primitive
x
atom-0876
atomic
1
x*log(15 - 2*x)
x \log{\left(15 - 2 x \right)}
\int x \log{\left(15 - 2 x \right)} \, dx
x**2*log(15 - 2*x)/2 - x**2/4 - 15*x/4 - 225*log(2*x - 15)/8
integration_primitive
x
atom-0877
atomic
1
-5*x*cos(2*x - 9)
- 5 x \cos{\left(2 x - 9 \right)}
\int - 5 x \cos{\left(2 x - 9 \right)} \, dx
-5*x*sin(2*x - 9)/2 - 5*cos(2*x - 9)/4
integration_primitive
x
atom-0878
atomic
1
3*x*exp(-9*x - 15)
3 x e^{- 9 x - 15}
\int 3 x e^{- 9 x - 15} \, dx
(-9*x - 1)*exp(-9*x - 15)/27
integration_primitive
x
atom-0879
atomic
1
-2*x*cos(8*x - 7)
- 2 x \cos{\left(8 x - 7 \right)}
\int - 2 x \cos{\left(8 x - 7 \right)} \, dx
-x*sin(8*x - 7)/4 - cos(8*x - 7)/32
integration_primitive
x
atom-0880
atomic
1
4*x*atan(3*x - 1)
4 x \operatorname{atan}{\left(3 x - 1 \right)}
\int 4 x \operatorname{atan}{\left(3 x - 1 \right)} \, dx
2*x**2*atan(3*x - 1) - 2*x/3 - 2*log(9*x**2 - 6*x + 2)/9
integration_primitive
x
atom-0881
atomic
1
-4*x*cos(11*x - 14)
- 4 x \cos{\left(11 x - 14 \right)}
\int - 4 x \cos{\left(11 x - 14 \right)} \, dx
-4*x*sin(11*x - 14)/11 - 4*cos(11*x - 14)/121
integration_primitive
x
atom-0882
atomic
1
2*x*atan(8*x + 1)
2 x \operatorname{atan}{\left(8 x + 1 \right)}
\int 2 x \operatorname{atan}{\left(8 x + 1 \right)} \, dx
x**2*atan(8*x + 1) - x/8 + log(32*x**2 + 8*x + 1)/64
integration_primitive
x
atom-0883
atomic
1
x*sin(13*x + 6)
x \sin{\left(13 x + 6 \right)}
\int x \sin{\left(13 x + 6 \right)} \, dx
-x*cos(13*x + 6)/13 + sin(13*x + 6)/169
integration_primitive
x
atom-0884
atomic
1
-2*x*sin(4*x - 9)
- 2 x \sin{\left(4 x - 9 \right)}
\int - 2 x \sin{\left(4 x - 9 \right)} \, dx
x*cos(4*x - 9)/2 - sin(4*x - 9)/8
integration_primitive
x
atom-0885
atomic
1
-x*sin(15*x + 8)
- x \sin{\left(15 x + 8 \right)}
\int - x \sin{\left(15 x + 8 \right)} \, dx
x*cos(15*x + 8)/15 - sin(15*x + 8)/225
integration_primitive
x
atom-0886
atomic
1
-3*x*exp(8 - 9*x)
- 3 x e^{8 - 9 x}
\int - 3 x e^{8 - 9 x} \, dx
(9*x + 1)*exp(8 - 9*x)/27
integration_primitive
x
atom-0887
atomic
1
-3*x*exp(-12*x - 4)
- 3 x e^{- 12 x - 4}
\int - 3 x e^{- 12 x - 4} \, dx
(12*x + 1)*exp(-12*x - 4)/48
integration_primitive
x
atom-0888
atomic
1
-5*x*atan(7*x - 9)
- 5 x \operatorname{atan}{\left(7 x - 9 \right)}
\int - 5 x \operatorname{atan}{\left(7 x - 9 \right)} \, dx
-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
integration_primitive
x
atom-0889
atomic
1
4*x*exp(6 - 14*x)
4 x e^{6 - 14 x}
\int 4 x e^{6 - 14 x} \, dx
(-14*x - 1)*exp(6 - 14*x)/49
integration_primitive
x
atom-0890
atomic
1
-5*x*exp(7 - 14*x)
- 5 x e^{7 - 14 x}
\int - 5 x e^{7 - 14 x} \, dx
(70*x + 5)*exp(7 - 14*x)/196
integration_primitive
x
atom-0891
atomic
1
x*cos(12*x - 2)
x \cos{\left(12 x - 2 \right)}
\int x \cos{\left(12 x - 2 \right)} \, dx
x*sin(12*x - 2)/12 + cos(12*x - 2)/144
integration_primitive
x
atom-0892
atomic
1
-3*x*exp(7 - 9*x)
- 3 x e^{7 - 9 x}
\int - 3 x e^{7 - 9 x} \, dx
(9*x + 1)*exp(7 - 9*x)/27
integration_primitive
x
atom-0893
atomic
1
-5*x*atan(12*x - 6)
- 5 x \operatorname{atan}{\left(12 x - 6 \right)}
\int - 5 x \operatorname{atan}{\left(12 x - 6 \right)} \, dx
-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
integration_primitive
x
atom-0894
atomic
1
4*x*log(7*x - 11)
4 x \log{\left(7 x - 11 \right)}
\int 4 x \log{\left(7 x - 11 \right)} \, dx
2*x**2*log(7*x - 11) - x**2 - 22*x/7 - 242*log(7*x - 11)/49
integration_primitive
x
atom-0895
atomic
1
-4*x*atan(x + 8)
- 4 x \operatorname{atan}{\left(x + 8 \right)}
\int - 4 x \operatorname{atan}{\left(x + 8 \right)} \, dx
-2*x**2*atan(x + 8) + 2*x - 16*log(x**2 + 16*x + 65) + 126*atan(x + 8)
integration_primitive
x
atom-0896
atomic
1
-4*x*log(10*x - 12)
- 4 x \log{\left(10 x - 12 \right)}
\int - 4 x \log{\left(10 x - 12 \right)} \, dx
-2*x**2*log(10*x - 12) + x**2 + 12*x/5 + 72*log(5*x - 6)/25
integration_primitive
x
atom-0897
atomic
1
-2*x*atan(9*x - 7)
- 2 x \operatorname{atan}{\left(9 x - 7 \right)}
\int - 2 x \operatorname{atan}{\left(9 x - 7 \right)} \, dx
-x**2*atan(9*x - 7) + x/9 + 7*log(81*x**2 - 126*x + 50)/81 + 16*atan(9*x - 7)/27
integration_primitive
x
atom-0898
atomic
1
x*exp(-6*x - 10)
x e^{- 6 x - 10}
\int x e^{- 6 x - 10} \, dx
(-6*x - 1)*exp(-6*x - 10)/36
integration_primitive
x
atom-0899
atomic
1
-2*x*log(7*x + 14)
- 2 x \log{\left(7 x + 14 \right)}
\int - 2 x \log{\left(7 x + 14 \right)} \, dx
-x**2*log(7*x + 14) + x**2/2 - 2*x + 4*log(x + 2)
integration_primitive
x