Integrand size = 219, antiderivative size = 26 \[ \int \frac {-41 x^2+40 x^3+e^x \left (41 x-32 x^2-8 x^3\right )+\left (50 x-58 x^2+e^x \left (-50+40 x+18 x^2\right )\right ) \log (x)+\left (10 x-10 e^x x\right ) \log ^2(x)+\left (-18 x^2+18 x^3+e^x \left (18 x-16 x^2-2 x^3\right )+\left (20 x-22 x^2+e^x \left (-20+18 x+4 x^2\right )\right ) \log (x)+\left (2 x-2 e^x x\right ) \log ^2(x)\right ) \log \left (-e^x+x\right )+\left (-2 x^2+2 x^3+e^x \left (2 x-2 x^2\right )+\left (2 x-2 x^2+e^x (-2+2 x)\right ) \log (x)\right ) \log ^2\left (-e^x+x\right )}{e^x x-x^2} \, dx=1+x-\left (x+(-x+\log (x)) \left (5+\log \left (-e^x+x\right )\right )\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(65\) vs. \(2(26)=52\).
Time = 0.23 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.50 \[ \int \frac {-41 x^2+40 x^3+e^x \left (41 x-32 x^2-8 x^3\right )+\left (50 x-58 x^2+e^x \left (-50+40 x+18 x^2\right )\right ) \log (x)+\left (10 x-10 e^x x\right ) \log ^2(x)+\left (-18 x^2+18 x^3+e^x \left (18 x-16 x^2-2 x^3\right )+\left (20 x-22 x^2+e^x \left (-20+18 x+4 x^2\right )\right ) \log (x)+\left (2 x-2 e^x x\right ) \log ^2(x)\right ) \log \left (-e^x+x\right )+\left (-2 x^2+2 x^3+e^x \left (2 x-2 x^2\right )+\left (2 x-2 x^2+e^x (-2+2 x)\right ) \log (x)\right ) \log ^2\left (-e^x+x\right )}{e^x x-x^2} \, dx=x-16 x^2+40 x \log (x)-25 \log ^2(x)-2 \left (4 x^2-9 x \log (x)+5 \log ^2(x)\right ) \log \left (-e^x+x\right )-(x-\log (x))^2 \log ^2\left (-e^x+x\right ) \]
Integrate[(-41*x^2 + 40*x^3 + E^x*(41*x - 32*x^2 - 8*x^3) + (50*x - 58*x^2 + E^x*(-50 + 40*x + 18*x^2))*Log[x] + (10*x - 10*E^x*x)*Log[x]^2 + (-18*x ^2 + 18*x^3 + E^x*(18*x - 16*x^2 - 2*x^3) + (20*x - 22*x^2 + E^x*(-20 + 18 *x + 4*x^2))*Log[x] + (2*x - 2*E^x*x)*Log[x]^2)*Log[-E^x + x] + (-2*x^2 + 2*x^3 + E^x*(2*x - 2*x^2) + (2*x - 2*x^2 + E^x*(-2 + 2*x))*Log[x])*Log[-E^ x + x]^2)/(E^x*x - x^2),x]
x - 16*x^2 + 40*x*Log[x] - 25*Log[x]^2 - 2*(4*x^2 - 9*x*Log[x] + 5*Log[x]^ 2)*Log[-E^x + x] - (x - Log[x])^2*Log[-E^x + x]^2
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {40 x^3-41 x^2+\left (-58 x^2+e^x \left (18 x^2+40 x-50\right )+50 x\right ) \log (x)+e^x \left (-8 x^3-32 x^2+41 x\right )+\left (2 x^3-2 x^2+e^x \left (2 x-2 x^2\right )+\left (-2 x^2+2 x+e^x (2 x-2)\right ) \log (x)\right ) \log ^2\left (x-e^x\right )+\left (18 x^3-18 x^2+\left (-22 x^2+e^x \left (4 x^2+18 x-20\right )+20 x\right ) \log (x)+e^x \left (-2 x^3-16 x^2+18 x\right )+\left (2 x-2 e^x x\right ) \log ^2(x)\right ) \log \left (x-e^x\right )+\left (10 x-10 e^x x\right ) \log ^2(x)}{e^x x-x^2} \, dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {-8 x^3-2 x^3 \log \left (x-e^x\right )-32 x^2-2 x^2 \log ^2\left (x-e^x\right )+18 x^2 \log (x)+4 x^2 \log (x) \log \left (x-e^x\right )-16 x^2 \log \left (x-e^x\right )+41 x-10 x \log ^2(x)+2 x \log (x) \log ^2\left (x-e^x\right )+2 x \log ^2\left (x-e^x\right )-2 x \log ^2(x) \log \left (x-e^x\right )-2 \log (x) \log ^2\left (x-e^x\right )+40 x \log (x)+18 x \log (x) \log \left (x-e^x\right )+18 x \log \left (x-e^x\right )-50 \log (x)-20 \log (x) \log \left (x-e^x\right )}{x}-\frac {2 (x-1) (x-\log (x)) \left (4 x+x \log \left (x-e^x\right )-5 \log (x)-\log (x) \log \left (x-e^x\right )\right )}{e^x-x}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {x^4}{6}-\frac {2}{3} \log (x) x^3-\frac {2}{3} \log \left (x-e^x\right ) x^3+\frac {5 x^3}{9}+2 \log (x) \log \left (x-e^x\right ) x^2-9 \log \left (x-e^x\right ) x^2-16 x^2-10 \log ^2(x) x+60 \log (x) x+18 \log (x) \log \left (x-e^x\right ) x-19 x-25 \log ^2(x)-4 \log (x) \log \left (x-e^x\right ) \int \frac {x}{e^x-x}dx+2 \log (x) \int \frac {x^2}{e^x-x}dx+4 \log (x) \log \left (x-e^x\right ) \int \frac {x^2}{e^x-x}dx+2 \log \left (x-e^x\right ) \int \frac {x^2}{e^x-x}dx-\int \frac {x^2}{e^x-x}dx-2 \log (x) \int \frac {x^3}{e^x-x}dx-2 \log \left (x-e^x\right ) \int \frac {x^3}{e^x-x}dx+\frac {1}{3} \int \frac {x^3}{e^x-x}dx+\frac {2}{3} \int \frac {x^4}{e^x-x}dx+10 \int \frac {\log ^2(x)}{e^x-x}dx-10 \int \frac {x \log ^2(x)}{e^x-x}dx-20 \int \frac {\log (x) \log \left (x-e^x\right )}{x}dx-2 \int \log ^2(x) \log \left (x-e^x\right )dx+2 \int \frac {\log ^2(x) \log \left (x-e^x\right )}{e^x-x}dx-2 \int \frac {x \log ^2(x) \log \left (x-e^x\right )}{e^x-x}dx+2 \int \log ^2\left (x-e^x\right )dx-2 \int x \log ^2\left (x-e^x\right )dx+2 \int \log (x) \log ^2\left (x-e^x\right )dx-2 \int \frac {\log (x) \log ^2\left (x-e^x\right )}{x}dx+4 \log (x) \int \int \frac {x}{e^x-x}dxdx-4 \log (x) \int \frac {\int \frac {x}{e^x-x}dx}{e^x-x}dx+4 \log \left (x-e^x\right ) \int \frac {\int \frac {x}{e^x-x}dx}{x}dx+4 \log (x) \int \frac {x \int \frac {x}{e^x-x}dx}{e^x-x}dx-4 \log (x) \int \int \frac {x^2}{e^x-x}dxdx-2 \int \int \frac {x^2}{e^x-x}dxdx+4 \log (x) \int \frac {\int \frac {x^2}{e^x-x}dx}{e^x-x}dx+2 \int \frac {\int \frac {x^2}{e^x-x}dx}{e^x-x}dx-4 \log \left (x-e^x\right ) \int \frac {\int \frac {x^2}{e^x-x}dx}{x}dx-2 \int \frac {\int \frac {x^2}{e^x-x}dx}{x}dx-4 \log (x) \int \frac {x \int \frac {x^2}{e^x-x}dx}{e^x-x}dx-2 \int \frac {x \int \frac {x^2}{e^x-x}dx}{e^x-x}dx+2 \int \int \frac {x^3}{e^x-x}dxdx-2 \int \frac {\int \frac {x^3}{e^x-x}dx}{e^x-x}dx+2 \int \frac {\int \frac {x^3}{e^x-x}dx}{x}dx+2 \int \frac {x \int \frac {x^3}{e^x-x}dx}{e^x-x}dx-4 \int \frac {\int \int \frac {x}{e^x-x}dxdx}{x}dx+4 \int \frac {\int \frac {\int \frac {x}{e^x-x}dx}{e^x-x}dx}{x}dx-4 \int \int \frac {\int \frac {x}{e^x-x}dx}{x}dxdx+4 \int \frac {\int \frac {\int \frac {x}{e^x-x}dx}{x}dx}{e^x-x}dx-4 \int \frac {x \int \frac {\int \frac {x}{e^x-x}dx}{x}dx}{e^x-x}dx-4 \int \frac {\int \frac {x \int \frac {x}{e^x-x}dx}{e^x-x}dx}{x}dx+4 \int \frac {\int \int \frac {x^2}{e^x-x}dxdx}{x}dx-4 \int \frac {\int \frac {\int \frac {x^2}{e^x-x}dx}{e^x-x}dx}{x}dx+4 \int \int \frac {\int \frac {x^2}{e^x-x}dx}{x}dxdx-4 \int \frac {\int \frac {\int \frac {x^2}{e^x-x}dx}{x}dx}{e^x-x}dx+4 \int \frac {x \int \frac {\int \frac {x^2}{e^x-x}dx}{x}dx}{e^x-x}dx+4 \int \frac {\int \frac {x \int \frac {x^2}{e^x-x}dx}{e^x-x}dx}{x}dx\) |
Int[(-41*x^2 + 40*x^3 + E^x*(41*x - 32*x^2 - 8*x^3) + (50*x - 58*x^2 + E^x *(-50 + 40*x + 18*x^2))*Log[x] + (10*x - 10*E^x*x)*Log[x]^2 + (-18*x^2 + 1 8*x^3 + E^x*(18*x - 16*x^2 - 2*x^3) + (20*x - 22*x^2 + E^x*(-20 + 18*x + 4 *x^2))*Log[x] + (2*x - 2*E^x*x)*Log[x]^2)*Log[-E^x + x] + (-2*x^2 + 2*x^3 + E^x*(2*x - 2*x^2) + (2*x - 2*x^2 + E^x*(-2 + 2*x))*Log[x])*Log[-E^x + x] ^2)/(E^x*x - x^2),x]
3.12.33.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(70\) vs. \(2(25)=50\).
Time = 0.31 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.73
| method | result | size |
| risch | \(\left (-x^{2}+2 x \ln \left (x \right )-\ln \left (x \right )^{2}\right ) \ln \left (x -{\mathrm e}^{x}\right )^{2}+\left (-8 x^{2}+18 x \ln \left (x \right )-10 \ln \left (x \right )^{2}\right ) \ln \left (x -{\mathrm e}^{x}\right )-16 x^{2}+40 x \ln \left (x \right )-25 \ln \left (x \right )^{2}+x\) | \(71\) |
| parallelrisch | \(-\ln \left (x \right )^{2} \ln \left (x -{\mathrm e}^{x}\right )^{2}+2 \ln \left (x \right ) \ln \left (x -{\mathrm e}^{x}\right )^{2} x -\ln \left (x -{\mathrm e}^{x}\right )^{2} x^{2}-10 \ln \left (x \right )^{2} \ln \left (x -{\mathrm e}^{x}\right )+18 \ln \left (x \right ) \ln \left (x -{\mathrm e}^{x}\right ) x -8 x^{2} \ln \left (x -{\mathrm e}^{x}\right )-25 \ln \left (x \right )^{2}+40 x \ln \left (x \right )-16 x^{2}+x\) | \(99\) |
int(((((-2+2*x)*exp(x)-2*x^2+2*x)*ln(x)+(-2*x^2+2*x)*exp(x)+2*x^3-2*x^2)*l n(x-exp(x))^2+((-2*exp(x)*x+2*x)*ln(x)^2+((4*x^2+18*x-20)*exp(x)-22*x^2+20 *x)*ln(x)+(-2*x^3-16*x^2+18*x)*exp(x)+18*x^3-18*x^2)*ln(x-exp(x))+(-10*exp (x)*x+10*x)*ln(x)^2+((18*x^2+40*x-50)*exp(x)-58*x^2+50*x)*ln(x)+(-8*x^3-32 *x^2+41*x)*exp(x)+40*x^3-41*x^2)/(exp(x)*x-x^2),x,method=_RETURNVERBOSE)
(-x^2+2*x*ln(x)-ln(x)^2)*ln(x-exp(x))^2+(-8*x^2+18*x*ln(x)-10*ln(x)^2)*ln( x-exp(x))-16*x^2+40*x*ln(x)-25*ln(x)^2+x
Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (27) = 54\).
Time = 0.26 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.62 \[ \int \frac {-41 x^2+40 x^3+e^x \left (41 x-32 x^2-8 x^3\right )+\left (50 x-58 x^2+e^x \left (-50+40 x+18 x^2\right )\right ) \log (x)+\left (10 x-10 e^x x\right ) \log ^2(x)+\left (-18 x^2+18 x^3+e^x \left (18 x-16 x^2-2 x^3\right )+\left (20 x-22 x^2+e^x \left (-20+18 x+4 x^2\right )\right ) \log (x)+\left (2 x-2 e^x x\right ) \log ^2(x)\right ) \log \left (-e^x+x\right )+\left (-2 x^2+2 x^3+e^x \left (2 x-2 x^2\right )+\left (2 x-2 x^2+e^x (-2+2 x)\right ) \log (x)\right ) \log ^2\left (-e^x+x\right )}{e^x x-x^2} \, dx=-{\left (x^{2} - 2 \, x \log \left (x\right ) + \log \left (x\right )^{2}\right )} \log \left (x - e^{x}\right )^{2} - 16 \, x^{2} - 2 \, {\left (4 \, x^{2} - 9 \, x \log \left (x\right ) + 5 \, \log \left (x\right )^{2}\right )} \log \left (x - e^{x}\right ) + 40 \, x \log \left (x\right ) - 25 \, \log \left (x\right )^{2} + x \]
integrate(((((-2+2*x)*exp(x)-2*x^2+2*x)*log(x)+(-2*x^2+2*x)*exp(x)+2*x^3-2 *x^2)*log(x-exp(x))^2+((-2*exp(x)*x+2*x)*log(x)^2+((4*x^2+18*x-20)*exp(x)- 22*x^2+20*x)*log(x)+(-2*x^3-16*x^2+18*x)*exp(x)+18*x^3-18*x^2)*log(x-exp(x ))+(-10*exp(x)*x+10*x)*log(x)^2+((18*x^2+40*x-50)*exp(x)-58*x^2+50*x)*log( x)+(-8*x^3-32*x^2+41*x)*exp(x)+40*x^3-41*x^2)/(exp(x)*x-x^2),x, algorithm= \
-(x^2 - 2*x*log(x) + log(x)^2)*log(x - e^x)^2 - 16*x^2 - 2*(4*x^2 - 9*x*lo g(x) + 5*log(x)^2)*log(x - e^x) + 40*x*log(x) - 25*log(x)^2 + x
Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (19) = 38\).
Time = 0.42 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.62 \[ \int \frac {-41 x^2+40 x^3+e^x \left (41 x-32 x^2-8 x^3\right )+\left (50 x-58 x^2+e^x \left (-50+40 x+18 x^2\right )\right ) \log (x)+\left (10 x-10 e^x x\right ) \log ^2(x)+\left (-18 x^2+18 x^3+e^x \left (18 x-16 x^2-2 x^3\right )+\left (20 x-22 x^2+e^x \left (-20+18 x+4 x^2\right )\right ) \log (x)+\left (2 x-2 e^x x\right ) \log ^2(x)\right ) \log \left (-e^x+x\right )+\left (-2 x^2+2 x^3+e^x \left (2 x-2 x^2\right )+\left (2 x-2 x^2+e^x (-2+2 x)\right ) \log (x)\right ) \log ^2\left (-e^x+x\right )}{e^x x-x^2} \, dx=- 16 x^{2} + 40 x \log {\left (x \right )} + x + \left (- 8 x^{2} + 18 x \log {\left (x \right )} - 10 \log {\left (x \right )}^{2}\right ) \log {\left (x - e^{x} \right )} + \left (- x^{2} + 2 x \log {\left (x \right )} - \log {\left (x \right )}^{2}\right ) \log {\left (x - e^{x} \right )}^{2} - 25 \log {\left (x \right )}^{2} \]
integrate(((((-2+2*x)*exp(x)-2*x**2+2*x)*ln(x)+(-2*x**2+2*x)*exp(x)+2*x**3 -2*x**2)*ln(x-exp(x))**2+((-2*exp(x)*x+2*x)*ln(x)**2+((4*x**2+18*x-20)*exp (x)-22*x**2+20*x)*ln(x)+(-2*x**3-16*x**2+18*x)*exp(x)+18*x**3-18*x**2)*ln( x-exp(x))+(-10*exp(x)*x+10*x)*ln(x)**2+((18*x**2+40*x-50)*exp(x)-58*x**2+5 0*x)*ln(x)+(-8*x**3-32*x**2+41*x)*exp(x)+40*x**3-41*x**2)/(exp(x)*x-x**2), x)
-16*x**2 + 40*x*log(x) + x + (-8*x**2 + 18*x*log(x) - 10*log(x)**2)*log(x - exp(x)) + (-x**2 + 2*x*log(x) - log(x)**2)*log(x - exp(x))**2 - 25*log(x )**2
Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (27) = 54\).
Time = 0.22 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.62 \[ \int \frac {-41 x^2+40 x^3+e^x \left (41 x-32 x^2-8 x^3\right )+\left (50 x-58 x^2+e^x \left (-50+40 x+18 x^2\right )\right ) \log (x)+\left (10 x-10 e^x x\right ) \log ^2(x)+\left (-18 x^2+18 x^3+e^x \left (18 x-16 x^2-2 x^3\right )+\left (20 x-22 x^2+e^x \left (-20+18 x+4 x^2\right )\right ) \log (x)+\left (2 x-2 e^x x\right ) \log ^2(x)\right ) \log \left (-e^x+x\right )+\left (-2 x^2+2 x^3+e^x \left (2 x-2 x^2\right )+\left (2 x-2 x^2+e^x (-2+2 x)\right ) \log (x)\right ) \log ^2\left (-e^x+x\right )}{e^x x-x^2} \, dx=-{\left (x^{2} - 2 \, x \log \left (x\right ) + \log \left (x\right )^{2}\right )} \log \left (x - e^{x}\right )^{2} - 16 \, x^{2} - 2 \, {\left (4 \, x^{2} - 9 \, x \log \left (x\right ) + 5 \, \log \left (x\right )^{2}\right )} \log \left (x - e^{x}\right ) + 40 \, x \log \left (x\right ) - 25 \, \log \left (x\right )^{2} + x \]
integrate(((((-2+2*x)*exp(x)-2*x^2+2*x)*log(x)+(-2*x^2+2*x)*exp(x)+2*x^3-2 *x^2)*log(x-exp(x))^2+((-2*exp(x)*x+2*x)*log(x)^2+((4*x^2+18*x-20)*exp(x)- 22*x^2+20*x)*log(x)+(-2*x^3-16*x^2+18*x)*exp(x)+18*x^3-18*x^2)*log(x-exp(x ))+(-10*exp(x)*x+10*x)*log(x)^2+((18*x^2+40*x-50)*exp(x)-58*x^2+50*x)*log( x)+(-8*x^3-32*x^2+41*x)*exp(x)+40*x^3-41*x^2)/(exp(x)*x-x^2),x, algorithm= \
-(x^2 - 2*x*log(x) + log(x)^2)*log(x - e^x)^2 - 16*x^2 - 2*(4*x^2 - 9*x*lo g(x) + 5*log(x)^2)*log(x - e^x) + 40*x*log(x) - 25*log(x)^2 + x
Leaf count of result is larger than twice the leaf count of optimal. 98 vs. \(2 (27) = 54\).
Time = 0.32 (sec) , antiderivative size = 98, normalized size of antiderivative = 3.77 \[ \int \frac {-41 x^2+40 x^3+e^x \left (41 x-32 x^2-8 x^3\right )+\left (50 x-58 x^2+e^x \left (-50+40 x+18 x^2\right )\right ) \log (x)+\left (10 x-10 e^x x\right ) \log ^2(x)+\left (-18 x^2+18 x^3+e^x \left (18 x-16 x^2-2 x^3\right )+\left (20 x-22 x^2+e^x \left (-20+18 x+4 x^2\right )\right ) \log (x)+\left (2 x-2 e^x x\right ) \log ^2(x)\right ) \log \left (-e^x+x\right )+\left (-2 x^2+2 x^3+e^x \left (2 x-2 x^2\right )+\left (2 x-2 x^2+e^x (-2+2 x)\right ) \log (x)\right ) \log ^2\left (-e^x+x\right )}{e^x x-x^2} \, dx=-x^{2} \log \left (x - e^{x}\right )^{2} + 2 \, x \log \left (x - e^{x}\right )^{2} \log \left (x\right ) - \log \left (x - e^{x}\right )^{2} \log \left (x\right )^{2} - 8 \, x^{2} \log \left (x - e^{x}\right ) + 18 \, x \log \left (x - e^{x}\right ) \log \left (x\right ) - 10 \, \log \left (x - e^{x}\right ) \log \left (x\right )^{2} - 16 \, x^{2} + 40 \, x \log \left (x\right ) - 25 \, \log \left (x\right )^{2} + x \]
integrate(((((-2+2*x)*exp(x)-2*x^2+2*x)*log(x)+(-2*x^2+2*x)*exp(x)+2*x^3-2 *x^2)*log(x-exp(x))^2+((-2*exp(x)*x+2*x)*log(x)^2+((4*x^2+18*x-20)*exp(x)- 22*x^2+20*x)*log(x)+(-2*x^3-16*x^2+18*x)*exp(x)+18*x^3-18*x^2)*log(x-exp(x ))+(-10*exp(x)*x+10*x)*log(x)^2+((18*x^2+40*x-50)*exp(x)-58*x^2+50*x)*log( x)+(-8*x^3-32*x^2+41*x)*exp(x)+40*x^3-41*x^2)/(exp(x)*x-x^2),x, algorithm= \
-x^2*log(x - e^x)^2 + 2*x*log(x - e^x)^2*log(x) - log(x - e^x)^2*log(x)^2 - 8*x^2*log(x - e^x) + 18*x*log(x - e^x)*log(x) - 10*log(x - e^x)*log(x)^2 - 16*x^2 + 40*x*log(x) - 25*log(x)^2 + x
Time = 8.08 (sec) , antiderivative size = 98, normalized size of antiderivative = 3.77 \[ \int \frac {-41 x^2+40 x^3+e^x \left (41 x-32 x^2-8 x^3\right )+\left (50 x-58 x^2+e^x \left (-50+40 x+18 x^2\right )\right ) \log (x)+\left (10 x-10 e^x x\right ) \log ^2(x)+\left (-18 x^2+18 x^3+e^x \left (18 x-16 x^2-2 x^3\right )+\left (20 x-22 x^2+e^x \left (-20+18 x+4 x^2\right )\right ) \log (x)+\left (2 x-2 e^x x\right ) \log ^2(x)\right ) \log \left (-e^x+x\right )+\left (-2 x^2+2 x^3+e^x \left (2 x-2 x^2\right )+\left (2 x-2 x^2+e^x (-2+2 x)\right ) \log (x)\right ) \log ^2\left (-e^x+x\right )}{e^x x-x^2} \, dx=x-25\,{\ln \left (x\right )}^2-\ln \left (x-{\mathrm {e}}^x\right )\,\left (18\,x-\frac {18\,x^2-8\,x^3}{x}+10\,{\ln \left (x\right )}^2-18\,x\,\ln \left (x\right )\right )-{\ln \left (x-{\mathrm {e}}^x\right )}^2\,\left (2\,x-\frac {2\,x^2-x^3}{x}+{\ln \left (x\right )}^2-2\,x\,\ln \left (x\right )\right )+40\,x\,\ln \left (x\right )-16\,x^2 \]
int((log(x)*(50*x + exp(x)*(40*x + 18*x^2 - 50) - 58*x^2) + log(x - exp(x) )*(log(x)*(20*x + exp(x)*(18*x + 4*x^2 - 20) - 22*x^2) + log(x)^2*(2*x - 2 *x*exp(x)) - 18*x^2 + 18*x^3 - exp(x)*(16*x^2 - 18*x + 2*x^3)) + log(x)^2* (10*x - 10*x*exp(x)) - 41*x^2 + 40*x^3 + log(x - exp(x))^2*(log(x)*(2*x + exp(x)*(2*x - 2) - 2*x^2) + exp(x)*(2*x - 2*x^2) - 2*x^2 + 2*x^3) - exp(x) *(32*x^2 - 41*x + 8*x^3))/(x*exp(x) - x^2),x)