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

Optimal. Leaf size=31 \[ x \log \left (\frac {x \left (-2 x+\frac {x}{-1-e^{20}}+\log (1-x)\right )}{1+x}\right ) \]

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Rubi [F]  time = 5.64, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \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 \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \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\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.14, size = 40, normalized size = 1.29 \begin {gather*} 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 ) \end {gather*}

Antiderivative was successfully verified.

[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))]

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fricas [A]  time = 0.76, size = 43, normalized size = 1.39 \begin {gather*} 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 ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

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giac [A]  time = 0.76, size = 48, normalized size = 1.55 \begin {gather*} 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 ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

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maple [C]  time = 0.59, size = 595, normalized size = 19.19

method	result	size
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 (x +1\right ) x +x \ln \relax (x )+\frac {i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {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 )}{x +1}\right )^{2}}{2}-\frac {i \pi x \,\mathrm {csgn}\left (\frac {i}{x +1}\right ) \mathrm {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 ) \mathrm {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 )}{x +1}\right )}{2}-\frac {i \pi x \,\mathrm {csgn}\left (i x \right ) \mathrm {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 )}{x +1}\right ) \mathrm {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 )}{x +1}\right )}{2}+\frac {i \pi x \mathrm {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 )}{x +1}\right )^{3}}{2}+\frac {i \pi x \,\mathrm {csgn}\left (\frac {i}{x +1}\right ) \mathrm {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 )}{x +1}\right )^{2}}{2}-\frac {i \pi x \,\mathrm {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 ) \mathrm {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 )}{x +1}\right )^{2}}{2}-\frac {i \pi x \,\mathrm {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 )}{x +1}\right ) \mathrm {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 )}{x +1}\right )^{2}}{2}-\frac {i \pi x \mathrm {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 )}{x +1}\right )^{3}}{2}+i x \pi -i \pi x \mathrm {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 )}{x +1}\right )^{2}-\ln \left ({\mathrm e}^{20}+1\right ) x +x \ln \relax (2)\)	\(595\)

Verification of antiderivative is not currently implemented for this CAS.

[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)/((x+1)*exp(20)+x+1))+((x-1)*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)*ex
p(20)+x^2-1)*ln(1-x)+(-2*x^3+2*x)*exp(20)-3*x^3+3*x),x,method=_RETURNVERBOSE)

[Out]

x*ln((x-1/2*ln(1-x))*exp(20)+3/2*x-1/2*ln(1-x))-ln(x+1)*x+x*ln(x)+1/2*I*Pi*x*csgn(I*x)*csgn(I*x*(-(x-1/2*ln(1-
x))*exp(20)-3/2*x+1/2*ln(1-x))/(x+1))^2-1/2*I*Pi*x*csgn(I/(x+1))*csgn(I*(-(x-1/2*ln(1-x))*exp(20)-3/2*x+1/2*ln
(1-x)))*csgn(I/(x+1)*(-(x-1/2*ln(1-x))*exp(20)-3/2*x+1/2*ln(1-x)))-1/2*I*Pi*x*csgn(I*x)*csgn(I/(x+1)*(-(x-1/2*
ln(1-x))*exp(20)-3/2*x+1/2*ln(1-x)))*csgn(I*x*(-(x-1/2*ln(1-x))*exp(20)-3/2*x+1/2*ln(1-x))/(x+1))+1/2*I*Pi*x*c
sgn(I/(x+1)*(-(x-1/2*ln(1-x))*exp(20)-3/2*x+1/2*ln(1-x)))^3+1/2*I*Pi*x*csgn(I/(x+1))*csgn(I/(x+1)*(-(x-1/2*ln(
1-x))*exp(20)-3/2*x+1/2*ln(1-x)))^2-1/2*I*Pi*x*csgn(I*(-(x-1/2*ln(1-x))*exp(20)-3/2*x+1/2*ln(1-x)))*csgn(I/(x+
1)*(-(x-1/2*ln(1-x))*exp(20)-3/2*x+1/2*ln(1-x)))^2-1/2*I*Pi*x*csgn(I/(x+1)*(-(x-1/2*ln(1-x))*exp(20)-3/2*x+1/2
*ln(1-x)))*csgn(I*x*(-(x-1/2*ln(1-x))*exp(20)-3/2*x+1/2*ln(1-x))/(x+1))^2-1/2*I*Pi*x*csgn(I*x*(-(x-1/2*ln(1-x)
)*exp(20)-3/2*x+1/2*ln(1-x))/(x+1))^3+I*Pi*x-I*Pi*x*csgn(I*x*(-(x-1/2*ln(1-x))*exp(20)-3/2*x+1/2*ln(1-x))/(x+1
))^2-ln(exp(20)+1)*x+x*ln(2)

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maxima [A]  time = 0.51, size = 60, normalized size = 1.94 \begin {gather*} -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 \relax (x) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

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mupad [B]  time = 4.24, size = 43, normalized size = 1.39 \begin {gather*} 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 ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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))

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sympy [A]  time = 1.23, size = 37, normalized size = 1.19 \begin {gather*} 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 )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

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