3.68.78 \(\int \frac {(e^5 x^2+e^5 x \log (8)) \log (-12 x^2-12 x \log (8))+(-16 x-4 x^2+(-8-2 x) \log (8)+(8 x+2 x^2+(8+2 x) \log (8)) \log (-12 x^2-12 x \log (8))) \log (\frac {x}{\log (-12 x^2-12 x \log (8))})+(x^2+x \log (8)) \log (-12 x^2-12 x \log (8)) \log ^2(\frac {x}{\log (-12 x^2-12 x \log (8))})}{(x^2+x \log (8)) \log (-12 x^2-12 x \log (8))} \, dx\)

Optimal. Leaf size=23 \[ (4+x) \left (e^5+\log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right )\right ) \]

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Rubi [F]  time = 5.94, 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 {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((E^5*x^2 + E^5*x*Log[8])*Log[-12*x^2 - 12*x*Log[8]] + (-16*x - 4*x^2 + (-8 - 2*x)*Log[8] + (8*x + 2*x^2 +
(8 + 2*x)*Log[8])*Log[-12*x^2 - 12*x*Log[8]])*Log[x/Log[-12*x^2 - 12*x*Log[8]]] + (x^2 + x*Log[8])*Log[-12*x^
2 - 12*x*Log[8]]*Log[x/Log[-12*x^2 - 12*x*Log[8]]]^2)/((x^2 + x*Log[8])*Log[-12*x^2 - 12*x*Log[8]]),x]

[Out]

E^5*x - (8*x)/Log[8] + (2*x*(4 - Log[8]))/Log[8] + (8*x*Log[x/Log[-12*x*(x + Log[8])]])/Log[8] - (2*x*(4 - Log
[8])*Log[x/Log[-12*x*(x + Log[8])]])/Log[8] - (8*Defer[Int][(-2*x - Log[8])/((x + Log[8])*Log[-12*x*(x + Log[8
])]), x])/Log[8] + (2*(4 - Log[8])*Defer[Int][(-2*x - Log[8])/((x + Log[8])*Log[-12*x*(x + Log[8])]), x])/Log[
8] + 8*Defer[Int][Log[x/Log[-12*x*(x + Log[8])]]/x, x] - (16*Defer[Int][Log[x/Log[-12*x*(x + Log[8])]]/Log[-12
*x*(x + Log[8])], x])/Log[8] + (4*(4 - Log[8])*Defer[Int][Log[x/Log[-12*x*(x + Log[8])]]/Log[-12*x*(x + Log[8]
)], x])/Log[8] - 8*Defer[Int][Log[x/Log[-12*x*(x + Log[8])]]/(x*Log[-12*x*(x + Log[8])]), x] - 2*(4 - Log[8])*
Defer[Int][Log[x/Log[-12*x*(x + Log[8])]]/((x + Log[8])*Log[-12*x*(x + Log[8])]), x] + Defer[Int][Log[x/Log[-1
2*x*(x + Log[8])]]^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{x (x+\log (8)) \log \left (-12 x^2-12 x \log (8)\right )} \, dx\\ &=\int \frac {e^5 x^2+e^5 x \log (8)+\frac {2 (4+x) (-2 x-\log (8)+(x+\log (8)) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))}+x (x+\log (8)) \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x (x+\log (8))} \, dx\\ &=\int \left (e^5+\frac {2 (4+x) (-2 x-\log (8)+x \log (-12 x (x+\log (8)))+\log (8) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x (x+\log (8)) \log (-12 x (x+\log (8)))}+\log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right )\right ) \, dx\\ &=e^5 x+2 \int \frac {(4+x) (-2 x-\log (8)+x \log (-12 x (x+\log (8)))+\log (8) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x (x+\log (8)) \log (-12 x (x+\log (8)))} \, dx+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x+2 \int \frac {(4+x) (-2 x-\log (8)+(x+\log (8)) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x (x+\log (8)) \log (-12 x (x+\log (8)))} \, dx+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x+2 \int \left (\frac {4 (-2 x-\log (8)+x \log (-12 x (x+\log (8)))+\log (8) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (8) \log (-12 x (x+\log (8)))}+\frac {(-4+\log (8)) (-2 x-\log (8)+x \log (-12 x (x+\log (8)))+\log (8) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (8) (x+\log (8)) \log (-12 x (x+\log (8)))}\right ) \, dx+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x+\frac {8 \int \frac {(-2 x-\log (8)+x \log (-12 x (x+\log (8)))+\log (8) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\frac {(2 (-4+\log (8))) \int \frac {(-2 x-\log (8)+x \log (-12 x (x+\log (8)))+\log (8) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x+\frac {8 \int \frac {(-2 x-\log (8)+(x+\log (8)) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\frac {(2 (-4+\log (8))) \int \frac {(-2 x-\log (8)+(x+\log (8)) \log (-12 x (x+\log (8)))) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x+\frac {8 \int \left (\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )+\frac {\log (8) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x}-\frac {2 \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))}-\frac {\log (8) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (-12 x (x+\log (8)))}\right ) \, dx}{\log (8)}+\frac {(2 (-4+\log (8))) \int \left (\frac {x \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x+\log (8)}+\frac {\log (8) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x+\log (8)}-\frac {2 x \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))}-\frac {\log (8) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))}\right ) \, dx}{\log (8)}+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x+8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x} \, dx-8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (-12 x (x+\log (8)))} \, dx+(2 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x+\log (8)} \, dx-(2 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx+\frac {8 \int \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx}{\log (8)}-\frac {16 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\frac {(2 (-4+\log (8))) \int \frac {x \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x+\log (8)} \, dx}{\log (8)}-\frac {(4 (-4+\log (8))) \int \frac {x \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x+\frac {8 x \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (8)}+8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x} \, dx-8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (-12 x (x+\log (8)))} \, dx+(2 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x+\log (8)} \, dx-(2 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx-\frac {8 \int \frac {-2 x-\log (8)+(x+\log (8)) \log (-12 x (x+\log (8)))}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx}{\log (8)}-\frac {16 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\frac {(2 (-4+\log (8))) \int \left (\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )-\frac {\log (8) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x+\log (8)}\right ) \, dx}{\log (8)}-\frac {(4 (-4+\log (8))) \int \left (\frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))}-\frac {\log (8) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))}\right ) \, dx}{\log (8)}+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x+\frac {8 x \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (8)}+8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x} \, dx-8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (-12 x (x+\log (8)))} \, dx-(4 (4-\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx-(2 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx-\frac {8 \int \left (1+\frac {-2 x-\log (8)}{(x+\log (8)) \log (-12 x (x+\log (8)))}\right ) \, dx}{\log (8)}-\frac {16 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\frac {(2 (-4+\log (8))) \int \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx}{\log (8)}-\frac {(4 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x-\frac {8 x}{\log (8)}+\frac {8 x \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (8)}-\frac {2 x (4-\log (8)) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (8)}+8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x} \, dx-8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (-12 x (x+\log (8)))} \, dx-(4 (4-\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx-(2 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx-\frac {8 \int \frac {-2 x-\log (8)}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx}{\log (8)}-\frac {16 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}-\frac {(2 (-4+\log (8))) \int \frac {-2 x-\log (8)+(x+\log (8)) \log (-12 x (x+\log (8)))}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx}{\log (8)}-\frac {(4 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x-\frac {8 x}{\log (8)}+\frac {8 x \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (8)}-\frac {2 x (4-\log (8)) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (8)}+8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x} \, dx-8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (-12 x (x+\log (8)))} \, dx-(4 (4-\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx-(2 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx-\frac {8 \int \frac {-2 x-\log (8)}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx}{\log (8)}-\frac {16 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}-\frac {(2 (-4+\log (8))) \int \left (1+\frac {-2 x-\log (8)}{(x+\log (8)) \log (-12 x (x+\log (8)))}\right ) \, dx}{\log (8)}-\frac {(4 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ &=e^5 x-\frac {8 x}{\log (8)}+\frac {2 x (4-\log (8))}{\log (8)}+\frac {8 x \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (8)}-\frac {2 x (4-\log (8)) \log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (8)}+8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x} \, dx-8 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{x \log (-12 x (x+\log (8)))} \, dx-(4 (4-\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx-(2 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx-\frac {8 \int \frac {-2 x-\log (8)}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx}{\log (8)}-\frac {16 \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}-\frac {(2 (-4+\log (8))) \int \frac {-2 x-\log (8)}{(x+\log (8)) \log (-12 x (x+\log (8)))} \, dx}{\log (8)}-\frac {(4 (-4+\log (8))) \int \frac {\log \left (\frac {x}{\log (-12 x (x+\log (8)))}\right )}{\log (-12 x (x+\log (8)))} \, dx}{\log (8)}+\int \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.32, size = 25, normalized size = 1.09 \begin {gather*} e^5 x+(4+x) \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((E^5*x^2 + E^5*x*Log[8])*Log[-12*x^2 - 12*x*Log[8]] + (-16*x - 4*x^2 + (-8 - 2*x)*Log[8] + (8*x + 2
*x^2 + (8 + 2*x)*Log[8])*Log[-12*x^2 - 12*x*Log[8]])*Log[x/Log[-12*x^2 - 12*x*Log[8]]] + (x^2 + x*Log[8])*Log[
-12*x^2 - 12*x*Log[8]]*Log[x/Log[-12*x^2 - 12*x*Log[8]]]^2)/((x^2 + x*Log[8])*Log[-12*x^2 - 12*x*Log[8]]),x]

[Out]

E^5*x + (4 + x)*Log[x/Log[-12*x*(x + Log[8])]]^2

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fricas [A]  time = 0.64, size = 28, normalized size = 1.22 \begin {gather*} {\left (x + 4\right )} \log \left (\frac {x}{\log \left (-12 \, x^{2} - 36 \, x \log \relax (2)\right )}\right )^{2} + x e^{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x*log(2)+x^2)*log(-36*x*log(2)-12*x^2)*log(x/log(-36*x*log(2)-12*x^2))^2+((3*(2*x+8)*log(2)+2*x^
2+8*x)*log(-36*x*log(2)-12*x^2)+3*(-2*x-8)*log(2)-4*x^2-16*x)*log(x/log(-36*x*log(2)-12*x^2))+(3*x*exp(5)*log(
2)+x^2*exp(5))*log(-36*x*log(2)-12*x^2))/(3*x*log(2)+x^2)/log(-36*x*log(2)-12*x^2),x, algorithm="fricas")

[Out]

(x + 4)*log(x/log(-12*x^2 - 36*x*log(2)))^2 + x*e^5

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (x^{2} + 3 \, x \log \relax (2)\right )} \log \left (-12 \, x^{2} - 36 \, x \log \relax (2)\right ) \log \left (\frac {x}{\log \left (-12 \, x^{2} - 36 \, x \log \relax (2)\right )}\right )^{2} + {\left (x^{2} e^{5} + 3 \, x e^{5} \log \relax (2)\right )} \log \left (-12 \, x^{2} - 36 \, x \log \relax (2)\right ) - 2 \, {\left (2 \, x^{2} + 3 \, {\left (x + 4\right )} \log \relax (2) - {\left (x^{2} + 3 \, {\left (x + 4\right )} \log \relax (2) + 4 \, x\right )} \log \left (-12 \, x^{2} - 36 \, x \log \relax (2)\right ) + 8 \, x\right )} \log \left (\frac {x}{\log \left (-12 \, x^{2} - 36 \, x \log \relax (2)\right )}\right )}{{\left (x^{2} + 3 \, x \log \relax (2)\right )} \log \left (-12 \, x^{2} - 36 \, x \log \relax (2)\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x*log(2)+x^2)*log(-36*x*log(2)-12*x^2)*log(x/log(-36*x*log(2)-12*x^2))^2+((3*(2*x+8)*log(2)+2*x^
2+8*x)*log(-36*x*log(2)-12*x^2)+3*(-2*x-8)*log(2)-4*x^2-16*x)*log(x/log(-36*x*log(2)-12*x^2))+(3*x*exp(5)*log(
2)+x^2*exp(5))*log(-36*x*log(2)-12*x^2))/(3*x*log(2)+x^2)/log(-36*x*log(2)-12*x^2),x, algorithm="giac")

[Out]

integrate(((x^2 + 3*x*log(2))*log(-12*x^2 - 36*x*log(2))*log(x/log(-12*x^2 - 36*x*log(2)))^2 + (x^2*e^5 + 3*x*
e^5*log(2))*log(-12*x^2 - 36*x*log(2)) - 2*(2*x^2 + 3*(x + 4)*log(2) - (x^2 + 3*(x + 4)*log(2) + 4*x)*log(-12*
x^2 - 36*x*log(2)) + 8*x)*log(x/log(-12*x^2 - 36*x*log(2))))/((x^2 + 3*x*log(2))*log(-12*x^2 - 36*x*log(2))),
x)

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maple [F]  time = 0.05, size = 0, normalized size = 0.00 \[\int \frac {\left (3 x \ln \relax (2)+x^{2}\right ) \ln \left (-36 x \ln \relax (2)-12 x^{2}\right ) \ln \left (\frac {x}{\ln \left (-36 x \ln \relax (2)-12 x^{2}\right )}\right )^{2}+\left (\left (3 \left (2 x +8\right ) \ln \relax (2)+2 x^{2}+8 x \right ) \ln \left (-36 x \ln \relax (2)-12 x^{2}\right )+3 \left (-2 x -8\right ) \ln \relax (2)-4 x^{2}-16 x \right ) \ln \left (\frac {x}{\ln \left (-36 x \ln \relax (2)-12 x^{2}\right )}\right )+\left (3 x \,{\mathrm e}^{5} \ln \relax (2)+x^{2} {\mathrm e}^{5}\right ) \ln \left (-36 x \ln \relax (2)-12 x^{2}\right )}{\left (3 x \ln \relax (2)+x^{2}\right ) \ln \left (-36 x \ln \relax (2)-12 x^{2}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*x*ln(2)+x^2)*ln(-36*x*ln(2)-12*x^2)*ln(x/ln(-36*x*ln(2)-12*x^2))^2+((3*(2*x+8)*ln(2)+2*x^2+8*x)*ln(-36
*x*ln(2)-12*x^2)+3*(-2*x-8)*ln(2)-4*x^2-16*x)*ln(x/ln(-36*x*ln(2)-12*x^2))+(3*x*exp(5)*ln(2)+x^2*exp(5))*ln(-3
6*x*ln(2)-12*x^2))/(3*x*ln(2)+x^2)/ln(-36*x*ln(2)-12*x^2),x)

[Out]

int(((3*x*ln(2)+x^2)*ln(-36*x*ln(2)-12*x^2)*ln(x/ln(-36*x*ln(2)-12*x^2))^2+((3*(2*x+8)*ln(2)+2*x^2+8*x)*ln(-36
*x*ln(2)-12*x^2)+3*(-2*x-8)*ln(2)-4*x^2-16*x)*ln(x/ln(-36*x*ln(2)-12*x^2))+(3*x*exp(5)*ln(2)+x^2*exp(5))*ln(-3
6*x*ln(2)-12*x^2))/(3*x*ln(2)+x^2)/ln(-36*x*ln(2)-12*x^2),x)

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maxima [C]  time = 0.56, size = 94, normalized size = 4.09 \begin {gather*} {\left (x + 4\right )} \log \left (i \, \pi + \log \relax (3) + 2 \, \log \relax (2) + \log \left (x + 3 \, \log \relax (2)\right ) + \log \relax (x)\right )^{2} + 3 \, e^{5} \log \relax (2) \log \left (x + 3 \, \log \relax (2)\right ) - 2 \, {\left (x + 4\right )} \log \left (i \, \pi + \log \relax (3) + 2 \, \log \relax (2) + \log \left (x + 3 \, \log \relax (2)\right ) + \log \relax (x)\right ) \log \relax (x) + {\left (x + 4\right )} \log \relax (x)^{2} - {\left (3 \, \log \relax (2) \log \left (x + 3 \, \log \relax (2)\right ) - x\right )} e^{5} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x*log(2)+x^2)*log(-36*x*log(2)-12*x^2)*log(x/log(-36*x*log(2)-12*x^2))^2+((3*(2*x+8)*log(2)+2*x^
2+8*x)*log(-36*x*log(2)-12*x^2)+3*(-2*x-8)*log(2)-4*x^2-16*x)*log(x/log(-36*x*log(2)-12*x^2))+(3*x*exp(5)*log(
2)+x^2*exp(5))*log(-36*x*log(2)-12*x^2))/(3*x*log(2)+x^2)/log(-36*x*log(2)-12*x^2),x, algorithm="maxima")

[Out]

(x + 4)*log(I*pi + log(3) + 2*log(2) + log(x + 3*log(2)) + log(x))^2 + 3*e^5*log(2)*log(x + 3*log(2)) - 2*(x +
4)*log(I*pi + log(3) + 2*log(2) + log(x + 3*log(2)) + log(x))*log(x) + (x + 4)*log(x)^2 - (3*log(2)*log(x + 3
*log(2)) - x)*e^5

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \left (-12\,x^2-36\,\ln \relax (2)\,x\right )\,\left (x^2+3\,\ln \relax (2)\,x\right )\,{\ln \left (\frac {x}{\ln \left (-12\,x^2-36\,\ln \relax (2)\,x\right )}\right )}^2+\left (\ln \left (-12\,x^2-36\,\ln \relax (2)\,x\right )\,\left (8\,x+3\,\ln \relax (2)\,\left (2\,x+8\right )+2\,x^2\right )-3\,\ln \relax (2)\,\left (2\,x+8\right )-16\,x-4\,x^2\right )\,\ln \left (\frac {x}{\ln \left (-12\,x^2-36\,\ln \relax (2)\,x\right )}\right )+\ln \left (-12\,x^2-36\,\ln \relax (2)\,x\right )\,\left ({\mathrm {e}}^5\,x^2+3\,{\mathrm {e}}^5\,\ln \relax (2)\,x\right )}{\ln \left (-12\,x^2-36\,\ln \relax (2)\,x\right )\,\left (x^2+3\,\ln \relax (2)\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(- 36*x*log(2) - 12*x^2)*(x^2*exp(5) + 3*x*exp(5)*log(2)) - log(x/log(- 36*x*log(2) - 12*x^2))*(16*x +
3*log(2)*(2*x + 8) - log(- 36*x*log(2) - 12*x^2)*(8*x + 3*log(2)*(2*x + 8) + 2*x^2) + 4*x^2) + log(- 36*x*log
(2) - 12*x^2)*log(x/log(- 36*x*log(2) - 12*x^2))^2*(3*x*log(2) + x^2))/(log(- 36*x*log(2) - 12*x^2)*(3*x*log(2
) + x^2)),x)

[Out]

int((log(- 36*x*log(2) - 12*x^2)*(x^2*exp(5) + 3*x*exp(5)*log(2)) - log(x/log(- 36*x*log(2) - 12*x^2))*(16*x +
3*log(2)*(2*x + 8) - log(- 36*x*log(2) - 12*x^2)*(8*x + 3*log(2)*(2*x + 8) + 2*x^2) + 4*x^2) + log(- 36*x*log
(2) - 12*x^2)*log(x/log(- 36*x*log(2) - 12*x^2))^2*(3*x*log(2) + x^2))/(log(- 36*x*log(2) - 12*x^2)*(3*x*log(2
) + x^2)), x)

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sympy [A]  time = 1.02, size = 27, normalized size = 1.17 \begin {gather*} x e^{5} + \left (x + 4\right ) \log {\left (\frac {x}{\log {\left (- 12 x^{2} - 36 x \log {\relax (2 )} \right )}} \right )}^{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*x*ln(2)+x**2)*ln(-36*x*ln(2)-12*x**2)*ln(x/ln(-36*x*ln(2)-12*x**2))**2+((3*(2*x+8)*ln(2)+2*x**2+
8*x)*ln(-36*x*ln(2)-12*x**2)+3*(-2*x-8)*ln(2)-4*x**2-16*x)*ln(x/ln(-36*x*ln(2)-12*x**2))+(3*x*exp(5)*ln(2)+x**
2*exp(5))*ln(-36*x*ln(2)-12*x**2))/(3*x*ln(2)+x**2)/ln(-36*x*ln(2)-12*x**2),x)

[Out]

x*exp(5) + (x + 4)*log(x/log(-12*x**2 - 36*x*log(2)))**2

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