\(\int \frac {7 x-2 x^2-3 x^3+e^{20} (5 x-x^2-2 x^3)+(-1+e^{20} (-1+x)+x) \log (1-x)+(3 x-3 x^3+e^{20} (2 x-2 x^3)+(-1+x^2+e^{20} (-1+x^2)) \log (1-x)) \log (\frac {-3 x^2-2 e^{20} x^2+(x+e^{20} x) \log (1-x)}{1+x+e^{20} (1+x)})}{3 x-3 x^3+e^{20} (2 x-2 x^3)+(-1+x^2+e^{20} (-1+x^2)) \log (1-x)} \, dx\) [5582]

Optimal result

Integrand size = 181, antiderivative size = 31 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log \left (\frac {x \left (-2 x+\frac {x}{-1-e^{20}}+\log (1-x)\right )}{1+x}\right ) \]

[Out]

x*ln((ln(1-x)+x/(-1-exp(20))-2*x)/(1+x)*x)

Rubi [F]

\[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=\int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx \]

[In]

Int[(7*x - 2*x^2 - 3*x^3 + E^20*(5*x - x^2 - 2*x^3) + (-1 + E^20*(-1 + x) + x)*Log[1 - x] + (3*x - 3*x^3 + E^2
0*(2*x - 2*x^3) + (-1 + x^2 + E^20*(-1 + x^2))*Log[1 - x])*Log[(-3*x^2 - 2*E^20*x^2 + (x + E^20*x)*Log[1 - x])
/(1 + x + E^20*(1 + x))])/(3*x - 3*x^3 + E^20*(2*x - 2*x^3) + (-1 + x^2 + E^20*(-1 + x^2))*Log[1 - x]),x]

[Out]

x*Log[-((x*((3 + 2*E^20)*x - (1 + E^20)*Log[1 - x]))/((1 + E^20)*(1 + x)))] + 2*Defer[Int][(3*(1 + (2*E^20)/3)
*x - (1 + E^20)*Log[1 - x])^(-1), x] + E^20*Defer[Int][(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log[1 - x])^(-1), x]
- (3 + 2*E^20)*Defer[Int][(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log[1 - x])^(-1), x] + (9*Defer[Int][1/((-1 - x)
*(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log[1 - x])), x])/2 + 2*E^20*Defer[Int][1/((-1 - x)*(3*(1 + (2*E^20)/3)*x
- (1 + E^20)*Log[1 - x])), x] - (3 + 2*E^20)*Defer[Int][1/((-1 - x)*(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log[1 -
x])), x] + (7*Defer[Int][1/((1 - x)*(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log[1 - x])), x])/2 + E^20*Defer[Int][
1/((1 - x)*(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log[1 - x])), x] - (1 + E^20)*Defer[Int][1/((1 - x)*(3*(1 + (2*E
^20)/3)*x - (1 + E^20)*Log[1 - x])), x] + (5*Defer[Int][1/((-1 + x)*(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log[1 -
x])), x])/2 + 3*Defer[Int][x/(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log[1 - x]), x] + 2*E^20*Defer[Int][x/(3*(1 +
(2*E^20)/3)*x - (1 + E^20)*Log[1 - x]), x] - (3 + 2*E^20)*Defer[Int][x/(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log
[1 - x]), x] + (3*Defer[Int][1/((1 + x)*(3*(1 + (2*E^20)/3)*x - (1 + E^20)*Log[1 - x])), x])/2 - (1 + E^20)*De
fer[Int][(-3*(1 + (2*E^20)/3)*x + (1 + E^20)*Log[1 - x])^(-1), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{\left (1-x^2\right ) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx \\ & = \int \left (\frac {7 x}{(1-x) (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {2 x^2}{(-1+x) (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {3 x^3}{(-1+x) (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {e^{20} x \left (5-x-2 x^2\right )}{(1-x) (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {\left (-1-e^{20}\right ) \log (1-x)}{(1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\log \left (\frac {x \left (-\left (\left (3+2 e^{20}\right ) x\right )+\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (1+x)}\right )\right ) \, dx \\ & = 2 \int \frac {x^2}{(-1+x) (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+3 \int \frac {x^3}{(-1+x) (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+7 \int \frac {x}{(1-x) (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+e^{20} \int \frac {x \left (5-x-2 x^2\right )}{(1-x) (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\left (-1-e^{20}\right ) \int \frac {\log (1-x)}{(1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\int \log \left (\frac {x \left (-\left (\left (3+2 e^{20}\right ) x\right )+\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (1+x)}\right ) \, dx \\ & = x \log \left (-\frac {x \left (\left (3+2 e^{20}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (1+x)}\right )+2 \int \left (\frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}+\frac {1}{\left (-1+x^2\right ) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}\right ) \, dx+3 \int \left (\frac {1}{2 (-1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}+\frac {1}{2 (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}\right ) \, dx+7 \int \left (\frac {1}{2 (-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {1}{2 (1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}\right ) \, dx+e^{20} \int \left (\frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}+\frac {2}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {2 x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}\right ) \, dx+\left (-1-e^{20}\right ) \int \left (-\frac {1}{\left (1+e^{20}\right ) (1+x)}+\frac {\left (3+2 e^{20}\right ) x}{\left (1+e^{20}\right ) (1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}\right ) \, dx-\int \frac {x \left (-7+2 x+3 x^2+e^{20} \left (-5+x+2 x^2\right )\right )-\left (1+e^{20}\right ) (-1+x) \log (1-x)}{(-1+x) (1+x) \left (\left (3+2 e^{20}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx \\ & = \log (1+x)+x \log \left (-\frac {x \left (\left (3+2 e^{20}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (1+x)}\right )+\frac {3}{2} \int \frac {1}{(-1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\frac {3}{2} \int \frac {1}{(1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+2 \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+2 \int \frac {1}{\left (-1+x^2\right ) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+3 \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\frac {7}{2} \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\frac {7}{2} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+e^{20} \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+e^{20} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\left (2 e^{20}\right ) \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\left (2 e^{20}\right ) \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\left (-3-2 e^{20}\right ) \int \frac {x}{(1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx-\int \left (\frac {1}{1+x}+\frac {x \left (4+3 e^{20}-\left (3+2 e^{20}\right ) x\right )}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}\right ) \, dx \\ & = x \log \left (-\frac {x \left (\left (3+2 e^{20}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (1+x)}\right )+\frac {3}{2} \int \frac {1}{(-1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\frac {3}{2} \int \frac {1}{(1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+2 \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+2 \int \left (\frac {1}{2 (-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {1}{2 (-1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}\right ) \, dx+3 \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\frac {7}{2} \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\frac {7}{2} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+e^{20} \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+e^{20} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\left (2 e^{20}\right ) \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\left (2 e^{20}\right ) \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\left (-3-2 e^{20}\right ) \int \left (\frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}+\frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}\right ) \, dx-\int \frac {x \left (4+3 e^{20}-\left (3+2 e^{20}\right ) x\right )}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx \\ & = x \log \left (-\frac {x \left (\left (3+2 e^{20}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (1+x)}\right )+\frac {3}{2} \int \frac {1}{(-1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\frac {3}{2} \int \frac {1}{(1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+2 \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+3 \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\frac {7}{2} \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\frac {7}{2} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+e^{20} \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+e^{20} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\left (2 e^{20}\right ) \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\left (2 e^{20}\right ) \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\left (-3-2 e^{20}\right ) \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\left (-3-2 e^{20}\right ) \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\int \frac {1}{(-1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx-\int \left (\frac {1+e^{20}}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}+\frac {\left (3+2 e^{20}\right ) x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)}+\frac {1+e^{20}}{-3 \left (1+\frac {2 e^{20}}{3}\right ) x+\left (1+e^{20}\right ) \log (1-x)}\right ) \, dx \\ & = x \log \left (-\frac {x \left (\left (3+2 e^{20}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (1+x)}\right )+\frac {3}{2} \int \frac {1}{(-1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\frac {3}{2} \int \frac {1}{(1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+2 \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+3 \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\frac {7}{2} \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\frac {7}{2} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+e^{20} \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+e^{20} \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\left (2 e^{20}\right ) \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\left (2 e^{20}\right ) \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\left (-3-2 e^{20}\right ) \int \frac {1}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\left (-3-2 e^{20}\right ) \int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx-\left (1+e^{20}\right ) \int \frac {1}{(1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx-\left (1+e^{20}\right ) \int \frac {1}{-3 \left (1+\frac {2 e^{20}}{3}\right ) x+\left (1+e^{20}\right ) \log (1-x)} \, dx-\left (3+2 e^{20}\right ) \int \frac {x}{3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)} \, dx+\int \frac {1}{(-1-x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx+\int \frac {1}{(-1+x) \left (3 \left (1+\frac {2 e^{20}}{3}\right ) x-\left (1+e^{20}\right ) \log (1-x)\right )} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.29 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log \left (\frac {x \left (-\left (\left (3+2 e^{20}\right ) x\right )+\left (1+e^{20}\right ) \log (1-x)\right )}{\left (1+e^{20}\right ) (1+x)}\right ) \]

[In]

Integrate[(7*x - 2*x^2 - 3*x^3 + E^20*(5*x - x^2 - 2*x^3) + (-1 + E^20*(-1 + x) + x)*Log[1 - x] + (3*x - 3*x^3
+ E^20*(2*x - 2*x^3) + (-1 + x^2 + E^20*(-1 + x^2))*Log[1 - x])*Log[(-3*x^2 - 2*E^20*x^2 + (x + E^20*x)*Log[1
- x])/(1 + x + E^20*(1 + x))])/(3*x - 3*x^3 + E^20*(2*x - 2*x^3) + (-1 + x^2 + E^20*(-1 + x^2))*Log[1 - x]),x
]

[Out]

x*Log[(x*(-((3 + 2*E^20)*x) + (1 + E^20)*Log[1 - x]))/((1 + E^20)*(1 + x))]

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(141\) vs. \(2(30)=60\).

Time = 4.83 (sec) , antiderivative size = 142, normalized size of antiderivative = 4.58

method	result	size
parallelrisch	\(-\frac {-{\mathrm e}^{40} x \ln \left (\frac {\left (x \,{\mathrm e}^{20}+x \right ) \ln \left (1-x \right )-2 x^{2} {\mathrm e}^{20}-3 x^{2}}{x \,{\mathrm e}^{20}+{\mathrm e}^{20}+x +1}\right )-2 \ln \left (\frac {\left (x \,{\mathrm e}^{20}+x \right ) \ln \left (1-x \right )-2 x^{2} {\mathrm e}^{20}-3 x^{2}}{x \,{\mathrm e}^{20}+{\mathrm e}^{20}+x +1}\right ) {\mathrm e}^{20} x -\ln \left (\frac {\left (x \,{\mathrm e}^{20}+x \right ) \ln \left (1-x \right )-2 x^{2} {\mathrm e}^{20}-3 x^{2}}{x \,{\mathrm e}^{20}+{\mathrm e}^{20}+x +1}\right ) x}{\left ({\mathrm e}^{20}+1\right )^{2}}\)	\(142\)
risch	\(x \ln \left (\left (x -\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}+\frac {3 x}{2}-\frac {\ln \left (1-x \right )}{2}\right )-\ln \left (1+x \right ) x +x \ln \left (x \right )-\frac {i \pi x {\operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{3}}{2}+\frac {i \pi x \,\operatorname {csgn}\left (i x \right ) {\operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}}{2}-\frac {i \pi x \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right ) \operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}{2}-\frac {i \pi x \,\operatorname {csgn}\left (i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )\right ) {\operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}}{2}-\frac {i \pi x \,\operatorname {csgn}\left (\frac {i}{1+x}\right ) \operatorname {csgn}\left (i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )\right ) \operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}{2}-\frac {i \pi x \,\operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right ) {\operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}}{2}+\frac {i \pi x \,\operatorname {csgn}\left (\frac {i}{1+x}\right ) {\operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}}{2}-i \pi x {\operatorname {csgn}\left (\frac {i x \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{2}+\frac {i \pi x {\operatorname {csgn}\left (\frac {i \left (\left (-x +\frac {\ln \left (1-x \right )}{2}\right ) {\mathrm e}^{20}-\frac {3 x}{2}+\frac {\ln \left (1-x \right )}{2}\right )}{1+x}\right )}^{3}}{2}+i x \pi -\ln \left ({\mathrm e}^{20}+1\right ) x +x \ln \left (2\right )\)	\(608\)

[In]

int(((((x^2-1)*exp(20)+x^2-1)*ln(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x)*ln(((x*exp(20)+x)*ln(1-x)-2*x^2*exp(20)-
3*x^2)/((1+x)*exp(20)+x+1))+((-1+x)*exp(20)+x-1)*ln(1-x)+(-2*x^3-x^2+5*x)*exp(20)-3*x^3-2*x^2+7*x)/(((x^2-1)*e
xp(20)+x^2-1)*ln(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x),x,method=_RETURNVERBOSE)

[Out]

-(-exp(20)^2*x*ln(((x*exp(20)+x)*ln(1-x)-2*x^2*exp(20)-3*x^2)/(x*exp(20)+exp(20)+x+1))-2*ln(((x*exp(20)+x)*ln(
1-x)-2*x^2*exp(20)-3*x^2)/(x*exp(20)+exp(20)+x+1))*exp(20)*x-ln(((x*exp(20)+x)*ln(1-x)-2*x^2*exp(20)-3*x^2)/(x
*exp(20)+exp(20)+x+1))*x)/(exp(20)+1)^2

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.39 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log \left (-\frac {2 \, x^{2} e^{20} + 3 \, x^{2} - {\left (x e^{20} + x\right )} \log \left (-x + 1\right )}{{\left (x + 1\right )} e^{20} + x + 1}\right ) \]

[In]

integrate(((((x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x)*log(((x*exp(20)+x)*log(1-x)-2*x^2
*exp(20)-3*x^2)/((1+x)*exp(20)+x+1))+((-1+x)*exp(20)+x-1)*log(1-x)+(-2*x^3-x^2+5*x)*exp(20)-3*x^3-2*x^2+7*x)/(
((x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x),x, algorithm="fricas")

[Out]

x*log(-(2*x^2*e^20 + 3*x^2 - (x*e^20 + x)*log(-x + 1))/((x + 1)*e^20 + x + 1))

Sympy [A] (verification not implemented)

Time = 0.63 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.19 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log {\left (\frac {- 2 x^{2} e^{20} - 3 x^{2} + \left (x + x e^{20}\right ) \log {\left (1 - x \right )}}{x + \left (x + 1\right ) e^{20} + 1} \right )} \]

[In]

integrate(((((x**2-1)*exp(20)+x**2-1)*ln(1-x)+(-2*x**3+2*x)*exp(20)-3*x**3+3*x)*ln(((x*exp(20)+x)*ln(1-x)-2*x*
*2*exp(20)-3*x**2)/((1+x)*exp(20)+x+1))+((-1+x)*exp(20)+x-1)*ln(1-x)+(-2*x**3-x**2+5*x)*exp(20)-3*x**3-2*x**2+
7*x)/(((x**2-1)*exp(20)+x**2-1)*ln(1-x)+(-2*x**3+2*x)*exp(20)-3*x**3+3*x),x)

[Out]

x*log((-2*x**2*exp(20) - 3*x**2 + (x + x*exp(20))*log(1 - x))/(x + (x + 1)*exp(20) + 1))

Maxima [A] (verification not implemented)

none

Time = 0.33 (sec) , antiderivative size = 60, normalized size of antiderivative = 1.94 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=-x {\left (\log \left (-e^{16} + e^{12} - e^{8} + e^{4} - 1\right ) + \log \left (e^{4} + 1\right )\right )} + x \log \left (x {\left (2 \, e^{20} + 3\right )} - {\left (e^{20} + 1\right )} \log \left (-x + 1\right )\right ) - x \log \left (x + 1\right ) + x \log \left (x\right ) \]

[In]

integrate(((((x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x)*log(((x*exp(20)+x)*log(1-x)-2*x^2
*exp(20)-3*x^2)/((1+x)*exp(20)+x+1))+((-1+x)*exp(20)+x-1)*log(1-x)+(-2*x^3-x^2+5*x)*exp(20)-3*x^3-2*x^2+7*x)/(
((x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x),x, algorithm="maxima")

[Out]

-x*(log(-e^16 + e^12 - e^8 + e^4 - 1) + log(e^4 + 1)) + x*log(x*(2*e^20 + 3) - (e^20 + 1)*log(-x + 1)) - x*log
(x + 1) + x*log(x)

Giac [A] (verification not implemented)

none

Time = 0.61 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.55 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x \log \left (-2 \, x^{2} e^{20} + x e^{20} \log \left (-x + 1\right ) - 3 \, x^{2} + x \log \left (-x + 1\right )\right ) - x \log \left (x e^{20} + x + e^{20} + 1\right ) \]

[In]

integrate(((((x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x)*log(((x*exp(20)+x)*log(1-x)-2*x^2
*exp(20)-3*x^2)/((1+x)*exp(20)+x+1))+((-1+x)*exp(20)+x-1)*log(1-x)+(-2*x^3-x^2+5*x)*exp(20)-3*x^3-2*x^2+7*x)/(
((x^2-1)*exp(20)+x^2-1)*log(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x),x, algorithm="giac")

[Out]

x*log(-2*x^2*e^20 + x*e^20*log(-x + 1) - 3*x^2 + x*log(-x + 1)) - x*log(x*e^20 + x + e^20 + 1)

Mupad [B] (verification not implemented)

Time = 11.58 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.39 \[ \int \frac {7 x-2 x^2-3 x^3+e^{20} \left (5 x-x^2-2 x^3\right )+\left (-1+e^{20} (-1+x)+x\right ) \log (1-x)+\left (3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)\right ) \log \left (\frac {-3 x^2-2 e^{20} x^2+\left (x+e^{20} x\right ) \log (1-x)}{1+x+e^{20} (1+x)}\right )}{3 x-3 x^3+e^{20} \left (2 x-2 x^3\right )+\left (-1+x^2+e^{20} \left (-1+x^2\right )\right ) \log (1-x)} \, dx=x\,\ln \left (-\frac {2\,x^2\,{\mathrm {e}}^{20}-\ln \left (1-x\right )\,\left (x+x\,{\mathrm {e}}^{20}\right )+3\,x^2}{x+{\mathrm {e}}^{20}\,\left (x+1\right )+1}\right ) \]

[In]

int((7*x - exp(20)*(x^2 - 5*x + 2*x^3) + log(-(2*x^2*exp(20) - log(1 - x)*(x + x*exp(20)) + 3*x^2)/(x + exp(20
)*(x + 1) + 1))*(3*x + exp(20)*(2*x - 2*x^3) + log(1 - x)*(x^2 + exp(20)*(x^2 - 1) - 1) - 3*x^3) + log(1 - x)*
(x + exp(20)*(x - 1) - 1) - 2*x^2 - 3*x^3)/(3*x + exp(20)*(2*x - 2*x^3) + log(1 - x)*(x^2 + exp(20)*(x^2 - 1)
- 1) - 3*x^3),x)

[Out]

x*log(-(2*x^2*exp(20) - log(1 - x)*(x + x*exp(20)) + 3*x^2)/(x + exp(20)*(x + 1) + 1))