\(\int \frac {(e^5 x^2+e^5 x \log (8)) \log (-12 x^2-12 x \log (8))+(-16 x-4 x^2+(-8-2 x) \log (8)+(8 x+2 x^2+(8+2 x) \log (8)) \log (-12 x^2-12 x \log (8))) \log (\frac {x}{\log (-12 x^2-12 x \log (8))})+(x^2+x \log (8)) \log (-12 x^2-12 x \log (8)) \log ^2(\frac {x}{\log (-12 x^2-12 x \log (8))})}{(x^2+x \log (8)) \log (-12 x^2-12 x \log (8))} \, dx\) [6778]

Optimal result

Integrand size = 159, antiderivative size = 23 \[ \int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx=(4+x) \left (e^5+\log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right )\right ) \]

[Out]

(ln(x/ln(-12*x*(3*ln(2)+x)))^2+exp(5))*(4+x)

Rubi [F]

\[ \int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx=\int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx \]

[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{align*} \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{align*}

Mathematica [A] (verified)

Time = 0.72 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.09 \[ \int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx=e^5 x+(4+x) \log ^2\left (\frac {x}{\log (-12 x (x+\log (8)))}\right ) \]

[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

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(49\) vs. \(2(24)=48\).

Time = 1.88 (sec) , antiderivative size = 50, normalized size of antiderivative = 2.17

method	result	size
parallelrisch	\(\ln \left (\frac {x}{\ln \left (-12 x \left (3 \ln \left (2\right )+x \right )\right )}\right )^{2} x -6 \,{\mathrm e}^{5} \ln \left (2\right )+x \,{\mathrm e}^{5}+4 \ln \left (\frac {x}{\ln \left (-12 x \left (3 \ln \left (2\right )+x \right )\right )}\right )^{2}\)	\(50\)

[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,method=_RETURNVERBOSE)

[Out]

ln(x/ln(-12*x*(3*ln(2)+x)))^2*x-6*exp(5)*ln(2)+x*exp(5)+4*ln(x/ln(-12*x*(3*ln(2)+x)))^2

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.22 \[ \int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx={\left (x + 4\right )} \log \left (\frac {x}{\log \left (-12 \, x^{2} - 36 \, x \log \left (2\right )\right )}\right )^{2} + x e^{5} \]

[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

Sympy [A] (verification not implemented)

Time = 0.41 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.17 \[ \int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx=x e^{5} + \left (x + 4\right ) \log {\left (\frac {x}{\log {\left (- 12 x^{2} - 36 x \log {\left (2 \right )} \right )}} \right )}^{2} \]

[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

Maxima [C] (verification not implemented)

Result contains complex when optimal does not.

Time = 0.36 (sec) , antiderivative size = 94, normalized size of antiderivative = 4.09 \[ \int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx={\left (x + 4\right )} \log \left (i \, \pi + \log \left (3\right ) + 2 \, \log \left (2\right ) + \log \left (x + 3 \, \log \left (2\right )\right ) + \log \left (x\right )\right )^{2} + 3 \, e^{5} \log \left (2\right ) \log \left (x + 3 \, \log \left (2\right )\right ) - 2 \, {\left (x + 4\right )} \log \left (i \, \pi + \log \left (3\right ) + 2 \, \log \left (2\right ) + \log \left (x + 3 \, \log \left (2\right )\right ) + \log \left (x\right )\right ) \log \left (x\right ) + {\left (x + 4\right )} \log \left (x\right )^{2} - {\left (3 \, \log \left (2\right ) \log \left (x + 3 \, \log \left (2\right )\right ) - x\right )} e^{5} \]

[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

Giac [F]

\[ \int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx=\int { \frac {{\left (x^{2} + 3 \, x \log \left (2\right )\right )} \log \left (-12 \, x^{2} - 36 \, x \log \left (2\right )\right ) \log \left (\frac {x}{\log \left (-12 \, x^{2} - 36 \, x \log \left (2\right )\right )}\right )^{2} + {\left (x^{2} e^{5} + 3 \, x e^{5} \log \left (2\right )\right )} \log \left (-12 \, x^{2} - 36 \, x \log \left (2\right )\right ) - 2 \, {\left (2 \, x^{2} + 3 \, {\left (x + 4\right )} \log \left (2\right ) - {\left (x^{2} + 3 \, {\left (x + 4\right )} \log \left (2\right ) + 4 \, x\right )} \log \left (-12 \, x^{2} - 36 \, x \log \left (2\right )\right ) + 8 \, x\right )} \log \left (\frac {x}{\log \left (-12 \, x^{2} - 36 \, x \log \left (2\right )\right )}\right )}{{\left (x^{2} + 3 \, x \log \left (2\right )\right )} \log \left (-12 \, x^{2} - 36 \, x \log \left (2\right )\right )} \,d x } \]

[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)

Mupad [F(-1)]

Timed out. \[ \int \frac {\left (e^5 x^2+e^5 x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )+\left (-16 x-4 x^2+(-8-2 x) \log (8)+\left (8 x+2 x^2+(8+2 x) \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )\right ) \log \left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )+\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right ) \log ^2\left (\frac {x}{\log \left (-12 x^2-12 x \log (8)\right )}\right )}{\left (x^2+x \log (8)\right ) \log \left (-12 x^2-12 x \log (8)\right )} \, dx=\int \frac {\ln \left (-12\,x^2-36\,\ln \left (2\right )\,x\right )\,\left (x^2+3\,\ln \left (2\right )\,x\right )\,{\ln \left (\frac {x}{\ln \left (-12\,x^2-36\,\ln \left (2\right )\,x\right )}\right )}^2+\left (\ln \left (-12\,x^2-36\,\ln \left (2\right )\,x\right )\,\left (8\,x+3\,\ln \left (2\right )\,\left (2\,x+8\right )+2\,x^2\right )-3\,\ln \left (2\right )\,\left (2\,x+8\right )-16\,x-4\,x^2\right )\,\ln \left (\frac {x}{\ln \left (-12\,x^2-36\,\ln \left (2\right )\,x\right )}\right )+\ln \left (-12\,x^2-36\,\ln \left (2\right )\,x\right )\,\left ({\mathrm {e}}^5\,x^2+3\,{\mathrm {e}}^5\,\ln \left (2\right )\,x\right )}{\ln \left (-12\,x^2-36\,\ln \left (2\right )\,x\right )\,\left (x^2+3\,\ln \left (2\right )\,x\right )} \,d x \]

[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)