3.3.21 \(\int \frac {e^{2 e^8+2 x+8 e^4 x+8 x^2+2 (2 e^4+4 x) \log (1-x+x^2)+2 \log ^2(1-x+x^2)} (-18+36 x+36 x^2+18 x^3+144 x^4+e^4 (36 x+72 x^3)+(36 x+72 x^3) \log (1-x+x^2))}{x^3-x^4+x^5} \, dx\)

Optimal. Leaf size=30 \[ \frac {9 e^{2 x+2 \left (e^4+2 x+\log (1+(-1+x) x)\right )^2}}{x^2} \]

________________________________________________________________________________________

Rubi [F]  time = 25.22, 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 {\exp \left (2 e^8+2 x+8 e^4 x+8 x^2+2 \left (2 e^4+4 x\right ) \log \left (1-x+x^2\right )+2 \log ^2\left (1-x+x^2\right )\right ) \left (-18+36 x+36 x^2+18 x^3+144 x^4+e^4 \left (36 x+72 x^3\right )+\left (36 x+72 x^3\right ) \log \left (1-x+x^2\right )\right )}{x^3-x^4+x^5} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(E^(2*E^8 + 2*x + 8*E^4*x + 8*x^2 + 2*(2*E^4 + 4*x)*Log[1 - x + x^2] + 2*Log[1 - x + x^2]^2)*(-18 + 36*x +
36*x^2 + 18*x^3 + 144*x^4 + E^4*(36*x + 72*x^3) + (36*x + 72*x^3)*Log[1 - x + x^2]))/(x^3 - x^4 + x^5),x]

[Out]

36*Defer[Int][(E^(2*(2*(1 + E^8/2) + (1 + 4*E^4)*x + 4*x^2 + 4*x*Log[1 - x + x^2] + Log[1 - x + x^2]^2))*(1 -
x + x^2)^(4*E^4))/x^2, x] + 36*Defer[Int][(E^(2*(2*(1 + E^8/2) + (1 + 4*E^4)*x + 4*x^2 + 4*x*Log[1 - x + x^2]
+ Log[1 - x + x^2]^2))*(1 - x + x^2)^(4*E^4))/x, x] + 18*Defer[Int][E^(2*(E^8 + (1 + 4*E^4)*x + 4*x^2 + 4*x*Lo
g[1 - x + x^2] + Log[1 - x + x^2]^2))*(1 - x + x^2)^(-1 + 4*E^4), x] + 72*Defer[Int][E^(2*(2*(1 + E^8/2) + (1
+ 4*E^4)*x + 4*x^2 + 4*x*Log[1 - x + x^2] + Log[1 - x + x^2]^2))*(1 - x + x^2)^(-1 + 4*E^4), x] - 18*Defer[Int
][(E^(2*(E^8 + (1 + 4*E^4)*x + 4*x^2 + 4*x*Log[1 - x + x^2] + Log[1 - x + x^2]^2))*(1 - x + x^2)^(-1 + 4*E^4))
/x^3, x] + 36*Defer[Int][(E^(2*(E^8 + (1 + 4*E^4)*x + 4*x^2 + 4*x*Log[1 - x + x^2] + Log[1 - x + x^2]^2))*(1 -
x + x^2)^(-1 + 4*E^4))/x^2, x] + 36*Defer[Int][(E^(2*(E^8 + (1 + 4*E^4)*x + 4*x^2 + 4*x*Log[1 - x + x^2] + Lo
g[1 - x + x^2]^2))*(1 - x + x^2)^(-1 + 4*E^4))/x, x] + 144*Defer[Int][E^(2*(E^8 + (1 + 4*E^4)*x + 4*x^2 + 4*x*
Log[1 - x + x^2] + Log[1 - x + x^2]^2))*x*(1 - x + x^2)^(-1 + 4*E^4), x] - 36*Defer[Int][E^(2*(2*(1 + E^8/2) +
(1 + 4*E^4)*x + 4*x^2 + 4*x*Log[1 - x + x^2] + Log[1 - x + x^2]^2))*x*(1 - x + x^2)^(-1 + 4*E^4), x] + 72*Def
er[Int][E^(2*(E^8 + (1 + 4*E^4)*x + 4*x^2 + 4*x*Log[1 - x + x^2] + Log[1 - x + x^2]^2))*(1 - x + x^2)^(-1 + 4*
E^4)*Log[1 - x + x^2], x] + 36*Defer[Int][(E^(2*(E^8 + (1 + 4*E^4)*x + 4*x^2 + 4*x*Log[1 - x + x^2] + Log[1 -
x + x^2]^2))*(1 - x + x^2)^(-1 + 4*E^4)*Log[1 - x + x^2])/x^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (2 e^8+2 x+8 e^4 x+8 x^2+2 \left (2 e^4+4 x\right ) \log \left (1-x+x^2\right )+2 \log ^2\left (1-x+x^2\right )\right ) \left (-18+36 x+36 x^2+18 x^3+144 x^4+e^4 \left (36 x+72 x^3\right )+\left (36 x+72 x^3\right ) \log \left (1-x+x^2\right )\right )}{x^3 \left (1-x+x^2\right )} \, dx\\ &=\int \left (\frac {18 \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{1-x+x^2}-\frac {18 \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x^3 \left (1-x+x^2\right )}+\frac {36 \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x^2 \left (1-x+x^2\right )}+\frac {36 \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x \left (1-x+x^2\right )}+\frac {144 \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) x}{1-x+x^2}+\frac {36 \exp \left (4+2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1+2 x^2\right )}{x^2 \left (1-x+x^2\right )}+\frac {36 \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1+2 x^2\right ) \log \left (1-x+x^2\right )}{x^2 \left (1-x+x^2\right )}\right ) \, dx\\ &=18 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{1-x+x^2} \, dx-18 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x^3 \left (1-x+x^2\right )} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x^2 \left (1-x+x^2\right )} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x \left (1-x+x^2\right )} \, dx+36 \int \frac {\exp \left (4+2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1+2 x^2\right )}{x^2 \left (1-x+x^2\right )} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1+2 x^2\right ) \log \left (1-x+x^2\right )}{x^2 \left (1-x+x^2\right )} \, dx+144 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) x}{1-x+x^2} \, dx\\ &=18 \int \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4} \, dx-18 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4}}{x^3} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4}}{x^2} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4}}{x} \, dx+36 \int \left (\frac {\exp \left (2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x^2}+\frac {\exp \left (2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x}+\frac {\exp \left (2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) (2-x)}{1-x+x^2}\right ) \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4} \left (1+2 x^2\right ) \log \left (1-x+x^2\right )}{x^2} \, dx+144 \int \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) x \left (1-x+x^2\right )^{-1+4 e^4} \, dx\\ &=18 \int \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4} \, dx-18 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4}}{x^3} \, dx+36 \int \frac {\exp \left (2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x^2} \, dx+36 \int \frac {\exp \left (2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right )}{x} \, dx+36 \int \frac {\exp \left (2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+2 e^4 \log \left (1-x+x^2\right )+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) (2-x)}{1-x+x^2} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4}}{x^2} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4}}{x} \, dx+36 \int \left (2 \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4} \log \left (1-x+x^2\right )+\frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4} \log \left (1-x+x^2\right )}{x^2}\right ) \, dx+144 \int \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) x \left (1-x+x^2\right )^{-1+4 e^4} \, dx\\ &=18 \int \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4} \, dx-18 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4}}{x^3} \, dx+36 \int \frac {\exp \left (2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{4 e^4}}{x^2} \, dx+36 \int \frac {\exp \left (2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{4 e^4}}{x} \, dx+36 \int \exp \left (2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) (2-x) \left (1-x+x^2\right )^{-1+4 e^4} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4}}{x^2} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4}}{x} \, dx+36 \int \frac {\exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4} \log \left (1-x+x^2\right )}{x^2} \, dx+72 \int \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) \left (1-x+x^2\right )^{-1+4 e^4} \log \left (1-x+x^2\right ) \, dx+144 \int \exp \left (2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )\right ) x \left (1-x+x^2\right )^{-1+4 e^4} \, dx\\ &=18 \int e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4} \, dx-18 \int \frac {e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4}}{x^3} \, dx+36 \int \frac {e^{2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{4 e^4}}{x^2} \, dx+36 \int \frac {e^{2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{4 e^4}}{x} \, dx+36 \int \frac {e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4}}{x^2} \, dx+36 \int \frac {e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4}}{x} \, dx+36 \int \left (2 e^{2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4}-e^{2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} x \left (1-x+x^2\right )^{-1+4 e^4}\right ) \, dx+36 \int \frac {e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4} \log \left (1-x+x^2\right )}{x^2} \, dx+72 \int e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4} \log \left (1-x+x^2\right ) \, dx+144 \int e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} x \left (1-x+x^2\right )^{-1+4 e^4} \, dx\\ &=18 \int e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4} \, dx-18 \int \frac {e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4}}{x^3} \, dx+36 \int \frac {e^{2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{4 e^4}}{x^2} \, dx+36 \int \frac {e^{2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{4 e^4}}{x} \, dx+36 \int \frac {e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4}}{x^2} \, dx+36 \int \frac {e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4}}{x} \, dx-36 \int e^{2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} x \left (1-x+x^2\right )^{-1+4 e^4} \, dx+36 \int \frac {e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4} \log \left (1-x+x^2\right )}{x^2} \, dx+72 \int e^{2 \left (2 \left (1+\frac {e^8}{2}\right )+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4} \, dx+72 \int e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{-1+4 e^4} \log \left (1-x+x^2\right ) \, dx+144 \int e^{2 \left (e^8+\left (1+4 e^4\right ) x+4 x^2+4 x \log \left (1-x+x^2\right )+\log ^2\left (1-x+x^2\right )\right )} x \left (1-x+x^2\right )^{-1+4 e^4} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.13, size = 54, normalized size = 1.80 \begin {gather*} \frac {9 e^{2 \left (e^8+x+4 e^4 x+4 x^2+\log ^2\left (1-x+x^2\right )\right )} \left (1-x+x^2\right )^{4 \left (e^4+2 x\right )}}{x^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(2*E^8 + 2*x + 8*E^4*x + 8*x^2 + 2*(2*E^4 + 4*x)*Log[1 - x + x^2] + 2*Log[1 - x + x^2]^2)*(-18 +
36*x + 36*x^2 + 18*x^3 + 144*x^4 + E^4*(36*x + 72*x^3) + (36*x + 72*x^3)*Log[1 - x + x^2]))/(x^3 - x^4 + x^5),
x]

[Out]

(9*E^(2*(E^8 + x + 4*E^4*x + 4*x^2 + Log[1 - x + x^2]^2))*(1 - x + x^2)^(4*(E^4 + 2*x)))/x^2

________________________________________________________________________________________

fricas [A]  time = 1.10, size = 54, normalized size = 1.80 \begin {gather*} \frac {9 \, e^{\left (8 \, x^{2} + 8 \, x e^{4} + 4 \, {\left (2 \, x + e^{4}\right )} \log \left (x^{2} - x + 1\right ) + 2 \, \log \left (x^{2} - x + 1\right )^{2} + 2 \, x + 2 \, e^{8}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x^3+36*x)*log(x^2-x+1)+(72*x^3+36*x)*exp(4)+144*x^4+18*x^3+36*x^2+36*x-18)*exp(log(x^2-x+1)^2+(
2*exp(4)+4*x)*log(x^2-x+1)+exp(4)^2+4*x*exp(4)+4*x^2+x)^2/(x^5-x^4+x^3),x, algorithm="fricas")

[Out]

9*e^(8*x^2 + 8*x*e^4 + 4*(2*x + e^4)*log(x^2 - x + 1) + 2*log(x^2 - x + 1)^2 + 2*x + 2*e^8)/x^2

________________________________________________________________________________________

giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {18 \, {\left (8 \, x^{4} + x^{3} + 2 \, x^{2} + 2 \, {\left (2 \, x^{3} + x\right )} e^{4} + 2 \, {\left (2 \, x^{3} + x\right )} \log \left (x^{2} - x + 1\right ) + 2 \, x - 1\right )} e^{\left (8 \, x^{2} + 8 \, x e^{4} + 4 \, {\left (2 \, x + e^{4}\right )} \log \left (x^{2} - x + 1\right ) + 2 \, \log \left (x^{2} - x + 1\right )^{2} + 2 \, x + 2 \, e^{8}\right )}}{x^{5} - x^{4} + x^{3}}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x^3+36*x)*log(x^2-x+1)+(72*x^3+36*x)*exp(4)+144*x^4+18*x^3+36*x^2+36*x-18)*exp(log(x^2-x+1)^2+(
2*exp(4)+4*x)*log(x^2-x+1)+exp(4)^2+4*x*exp(4)+4*x^2+x)^2/(x^5-x^4+x^3),x, algorithm="giac")

[Out]

integrate(18*(8*x^4 + x^3 + 2*x^2 + 2*(2*x^3 + x)*e^4 + 2*(2*x^3 + x)*log(x^2 - x + 1) + 2*x - 1)*e^(8*x^2 + 8
*x*e^4 + 4*(2*x + e^4)*log(x^2 - x + 1) + 2*log(x^2 - x + 1)^2 + 2*x + 2*e^8)/(x^5 - x^4 + x^3), x)

________________________________________________________________________________________

maple [B]  time = 0.05, size = 57, normalized size = 1.90

method	result	size
risch	\(\frac {9 \left (x^{2}-x +1\right )^{4 \,{\mathrm e}^{4}+8 x} {\mathrm e}^{2 \ln \left (x^{2}-x +1\right )^{2}+2 \,{\mathrm e}^{8}+8 x \,{\mathrm e}^{4}+8 x^{2}+2 x}}{x^{2}}\)	\(57\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((72*x^3+36*x)*ln(x^2-x+1)+(72*x^3+36*x)*exp(4)+144*x^4+18*x^3+36*x^2+36*x-18)*exp(ln(x^2-x+1)^2+(2*exp(4)
+4*x)*ln(x^2-x+1)+exp(4)^2+4*x*exp(4)+4*x^2+x)^2/(x^5-x^4+x^3),x,method=_RETURNVERBOSE)

[Out]

9/x^2*((x^2-x+1)^(2*exp(4)+4*x))^2*exp(2*ln(x^2-x+1)^2+2*exp(8)+8*x*exp(4)+8*x^2+2*x)

________________________________________________________________________________________

maxima [B]  time = 0.82, size = 62, normalized size = 2.07 \begin {gather*} \frac {9 \, e^{\left (8 \, x^{2} + 8 \, x e^{4} + 8 \, x \log \left (x^{2} - x + 1\right ) + 4 \, e^{4} \log \left (x^{2} - x + 1\right ) + 2 \, \log \left (x^{2} - x + 1\right )^{2} + 2 \, x + 2 \, e^{8}\right )}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x^3+36*x)*log(x^2-x+1)+(72*x^3+36*x)*exp(4)+144*x^4+18*x^3+36*x^2+36*x-18)*exp(log(x^2-x+1)^2+(
2*exp(4)+4*x)*log(x^2-x+1)+exp(4)^2+4*x*exp(4)+4*x^2+x)^2/(x^5-x^4+x^3),x, algorithm="maxima")

[Out]

9*e^(8*x^2 + 8*x*e^4 + 8*x*log(x^2 - x + 1) + 4*e^4*log(x^2 - x + 1) + 2*log(x^2 - x + 1)^2 + 2*x + 2*e^8)/x^2

________________________________________________________________________________________

mupad [B]  time = 0.78, size = 57, normalized size = 1.90 \begin {gather*} \frac {9\,{\mathrm {e}}^{2\,{\mathrm {e}}^8}\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{8\,x^2}\,{\mathrm {e}}^{2\,{\ln \left (x^2-x+1\right )}^2}\,{\mathrm {e}}^{8\,x\,{\mathrm {e}}^4}\,{\left (x^2-x+1\right )}^{8\,x+4\,{\mathrm {e}}^4}}{x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(2*x + 2*exp(8) + 8*x*exp(4) + 2*log(x^2 - x + 1)*(4*x + 2*exp(4)) + 8*x^2 + 2*log(x^2 - x + 1)^2)*(36
*x + exp(4)*(36*x + 72*x^3) + log(x^2 - x + 1)*(36*x + 72*x^3) + 36*x^2 + 18*x^3 + 144*x^4 - 18))/(x^3 - x^4 +
x^5),x)

[Out]

(9*exp(2*exp(8))*exp(2*x)*exp(8*x^2)*exp(2*log(x^2 - x + 1)^2)*exp(8*x*exp(4))*(x^2 - x + 1)^(8*x + 4*exp(4)))
/x^2

________________________________________________________________________________________

sympy [B]  time = 0.54, size = 56, normalized size = 1.87 \begin {gather*} \frac {9 e^{8 x^{2} + 2 x + 8 x e^{4} + 2 \left (4 x + 2 e^{4}\right ) \log {\left (x^{2} - x + 1 \right )} + 2 \log {\left (x^{2} - x + 1 \right )}^{2} + 2 e^{8}}}{x^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((72*x**3+36*x)*ln(x**2-x+1)+(72*x**3+36*x)*exp(4)+144*x**4+18*x**3+36*x**2+36*x-18)*exp(ln(x**2-x+1
)**2+(2*exp(4)+4*x)*ln(x**2-x+1)+exp(4)**2+4*x*exp(4)+4*x**2+x)**2/(x**5-x**4+x**3),x)

[Out]

9*exp(8*x**2 + 2*x + 8*x*exp(4) + 2*(4*x + 2*exp(4))*log(x**2 - x + 1) + 2*log(x**2 - x + 1)**2 + 2*exp(8))/x*
*2

________________________________________________________________________________________