\(\int \frac {(-32 x^2+16 x^3+e^2 (8 x-6 x^2)+(-16 x^2+4 x^3+e^2 (8 x-2 x^2)) \log (32 x^2-16 x^3+2 x^4+e^2 (-16 x+8 x^2-x^3))) \log (\frac {5}{x \log (32 x^2-16 x^3+2 x^4+e^2 (-16 x+8 x^2-x^3))})+(16 x^2-4 x^3+e^2 (-8 x+2 x^2)) \log (32 x^2-16 x^3+2 x^4+e^2 (-16 x+8 x^2-x^3)) \log ^2(\frac {5}{x \log (32 x^2-16 x^3+2 x^4+e^2 (-16 x+8 x^2-x^3))})}{(e^2 (-4+x)+8 x-2 x^2) \log (32 x^2-16 x^3+2 x^4+e^2 (-16 x+8 x^2-x^3))} \, dx\) [3697]

Optimal result

Integrand size = 290, antiderivative size = 33 \[ \int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx=x^2 \log ^2\left (\frac {5}{x \log \left ((4-x)^2 x \left (-e^2+2 x\right )\right )}\right ) \]

[Out]

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

Rubi [F]

\[ \int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx=\int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx \]

[In]

Int[((-32*x^2 + 16*x^3 + E^2*(8*x - 6*x^2) + (-16*x^2 + 4*x^3 + E^2*(8*x - 2*x^2))*Log[32*x^2 - 16*x^3 + 2*x^4
+ E^2*(-16*x + 8*x^2 - x^3)])*Log[5/(x*Log[32*x^2 - 16*x^3 + 2*x^4 + E^2*(-16*x + 8*x^2 - x^3)])] + (16*x^2 -
4*x^3 + E^2*(-8*x + 2*x^2))*Log[32*x^2 - 16*x^3 + 2*x^4 + E^2*(-16*x + 8*x^2 - x^3)]*Log[5/(x*Log[32*x^2 - 16
*x^3 + 2*x^4 + E^2*(-16*x + 8*x^2 - x^3)])]^2)/((E^2*(-4 + x) + 8*x - 2*x^2)*Log[32*x^2 - 16*x^3 + 2*x^4 + E^2
*(-16*x + 8*x^2 - x^3)]),x]

[Out]

(-64*x)/(8 - E^2) + (E^4*x)/(8 - E^2) + (8*(8 + E^2)*x)/(8 - E^2) - (E^2*(8 + E^2)*x)/(8 - E^2) - (4*x^2)/(8 -
E^2) + (E^2*x^2)/(2*(8 - E^2)) - (64*x*Log[5/(x*Log[-((E^2 - 2*x)*(4 - x)^2*x)])])/(8 - E^2) + (E^4*x*Log[5/(
x*Log[-((E^2 - 2*x)*(4 - x)^2*x)])])/(8 - E^2) + (8*(8 + E^2)*x*Log[5/(x*Log[-((E^2 - 2*x)*(4 - x)^2*x)])])/(8
- E^2) - (E^2*(8 + E^2)*x*Log[5/(x*Log[-((E^2 - 2*x)*(4 - x)^2*x)])])/(8 - E^2) - (8*x^2*Log[5/(x*Log[-((E^2
- 2*x)*(4 - x)^2*x)])])/(8 - E^2) + (E^2*x^2*Log[5/(x*Log[-((E^2 - 2*x)*(4 - x)^2*x)])])/(8 - E^2) - (256*Defe
r[Int][Log[-((E^2 - 2*x)*(-4 + x)^2*x)]^(-1), x])/(8 - E^2) + (4*E^4*Defer[Int][Log[-((E^2 - 2*x)*(-4 + x)^2*x
)]^(-1), x])/(8 - E^2) + (32*(8 + E^2)*Defer[Int][Log[-((E^2 - 2*x)*(-4 + x)^2*x)]^(-1), x])/(8 - E^2) - (4*E^
2*(8 + E^2)*Defer[Int][Log[-((E^2 - 2*x)*(-4 + x)^2*x)]^(-1), x])/(8 - E^2) - (4*(16 + E^2)*Defer[Int][Log[-((
E^2 - 2*x)*(-4 + x)^2*x)]^(-1), x])/(8 - E^2) + (E^2*(16 + E^2)*Defer[Int][Log[-((E^2 - 2*x)*(-4 + x)^2*x)]^(-
1), x])/(2*(8 - E^2)) + (64*E^2*Defer[Int][1/((E^2 - 2*x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 - E^2) + (
4*E^4*Defer[Int][1/((E^2 - 2*x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 - E^2) - (3*E^6*Defer[Int][1/((E^2 -
2*x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(2*(8 - E^2)) - (8*E^2*(8 + E^2)*Defer[Int][1/((E^2 - 2*x)*Log[-(
(E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 - E^2) + (E^4*(8 + E^2)*Defer[Int][1/((E^2 - 2*x)*Log[-((E^2 - 2*x)*(-4 +
x)^2*x)]), x])/(8 - E^2) - (768*Defer[Int][1/((-4 + x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 - E^2) + (32*
E^2*Defer[Int][1/((-4 + x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 - E^2) + (8*E^4*Defer[Int][1/((-4 + x)*Lo
g[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 - E^2) + (64*(8 + E^2)*Defer[Int][1/((-4 + x)*Log[-((E^2 - 2*x)*(-4 +
x)^2*x)]), x])/(8 - E^2) - (8*E^2*(8 + E^2)*Defer[Int][1/((-4 + x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 -
E^2) - (32*Defer[Int][x/Log[-((E^2 - 2*x)*(-4 + x)^2*x)], x])/(8 - E^2) + (4*E^2*Defer[Int][x/Log[-((E^2 - 2*
x)*(-4 + x)^2*x)], x])/(8 - E^2) - (8*E^4*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/(E^2 - 2*x),
x])/(8 - E^2) - (E^6*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/(E^2 - 2*x), x])/(8 - E^2) + (E^4*
(8 + E^2)*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/(E^2 - 2*x), x])/(8 - E^2) - (256*Defer[Int][
Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/(-4 + x), x])/(8 - E^2) - (32*E^2*Defer[Int][Log[5/(x*Log[-((E^2 -
2*x)*(-4 + x)^2*x)])]/(-4 + x), x])/(8 - E^2) + (32*(8 + E^2)*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^
2*x)])]/(-4 + x), x])/(8 - E^2) - (256*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/Log[-((E^2 - 2*x
)*(-4 + x)^2*x)], x])/(8 - E^2) + (4*E^4*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/Log[-((E^2 - 2
*x)*(-4 + x)^2*x)], x])/(8 - E^2) + (8*(16 + 3*E^2)*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/Log
[-((E^2 - 2*x)*(-4 + x)^2*x)], x])/(8 - E^2) - (E^2*(16 + 3*E^2)*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x
)^2*x)])]/Log[-((E^2 - 2*x)*(-4 + x)^2*x)], x])/(8 - E^2) - (8*E^4*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 +
x)^2*x)])]/((E^2 - 2*x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 - E^2) - (4*E^6*Defer[Int][Log[5/(x*Log[-((
E^2 - 2*x)*(-4 + x)^2*x)])]/((E^2 - 2*x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 - E^2) + (E^4*(16 + 3*E^2)*
Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/((E^2 - 2*x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8
- E^2) - (1024*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/((-4 + x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x
)]), x])/(8 - E^2) - (32*E^2*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/((-4 + x)*Log[-((E^2 - 2*x
)*(-4 + x)^2*x)]), x])/(8 - E^2) + (32*(16 + 3*E^2)*Defer[Int][Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x)^2*x)])]/((-
4 + x)*Log[-((E^2 - 2*x)*(-4 + x)^2*x)]), x])/(8 - E^2) - (64*Defer[Int][(x*Log[5/(x*Log[-((E^2 - 2*x)*(-4 + x
)^2*x)])])/Log[-((E^2 - 2*x)*(-4 + x)^2*x)], x])/(8 - E^2) + (8*E^2*Defer[Int][(x*Log[5/(x*Log[-((E^2 - 2*x)*(
-4 + x)^2*x)])])/Log[-((E^2 - 2*x)*(-4 + x)^2*x)], x])/(8 - E^2) + 2*Defer[Int][x*Log[5/(x*Log[-((E^2 - 2*x)*(
-4 + x)^2*x)])]^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \left (\frac {2 x \left (-8 (-2+x) x+e^2 (-4+3 x)+\left (e^2-2 x\right ) (-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right )}{\log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}+2 (-4+x) x \left (-e^2+2 x\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )\right )}{\left (e^2-2 x\right ) (4-x)} \, dx \\ & = \int \left (\frac {2 x \left (-4 e^2+16 \left (1+\frac {3 e^2}{16}\right ) x-8 x^2-4 e^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )+8 \left (1+\frac {e^2}{8}\right ) x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )-2 x^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) (4-x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}+2 x \log ^2\left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )\right ) \, dx \\ & = 2 \int \frac {x \left (-4 e^2+16 \left (1+\frac {3 e^2}{16}\right ) x-8 x^2-4 e^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )+8 \left (1+\frac {e^2}{8}\right ) x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )-2 x^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) (4-x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx+2 \int x \log ^2\left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx \\ & = 2 \int \frac {x \left (-e^2 (4-3 x)-8 (-2+x) x+\left (e^2-2 x\right ) (-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) (4-x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx+2 \int x \log ^2\left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx \\ & = 2 \int x \log ^2\left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx+2 \int \left (\frac {e^2 \left (-4 e^2+16 \left (1+\frac {3 e^2}{16}\right ) x-8 x^2-4 e^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )+8 \left (1+\frac {e^2}{8}\right ) x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )-2 x^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (8-e^2\right ) \left (e^2-2 x\right ) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}+\frac {4 \left (4 e^2-16 \left (1+\frac {3 e^2}{16}\right ) x+8 x^2+4 e^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )-8 \left (1+\frac {e^2}{8}\right ) x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )+2 x^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (8-e^2\right ) (4-x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx \\ & = 2 \int x \log ^2\left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx+\frac {8 \int \frac {\left (4 e^2-16 \left (1+\frac {3 e^2}{16}\right ) x+8 x^2+4 e^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )-8 \left (1+\frac {e^2}{8}\right ) x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )+2 x^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{(4-x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2}+\frac {\left (2 e^2\right ) \int \frac {\left (-4 e^2+16 \left (1+\frac {3 e^2}{16}\right ) x-8 x^2-4 e^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )+8 \left (1+\frac {e^2}{8}\right ) x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )-2 x^2 \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2} \\ & = 2 \int x \log ^2\left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx+\frac {8 \int \frac {\left (8 (-2+x) x-e^2 (-4+3 x)-\left (e^2-2 x\right ) (-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{(4-x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2}+\frac {\left (2 e^2\right ) \int \frac {\left (-8 (-2+x) x+e^2 (-4+3 x)+\left (e^2-2 x\right ) (-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )\right ) \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2} \\ & = 2 \int x \log ^2\left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx+\frac {8 \int \left (-\frac {4 e^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{-4+x}+\frac {8 \left (1+\frac {e^2}{8}\right ) x \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{-4+x}-\frac {2 x^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{-4+x}-\frac {4 e^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{(-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}+\frac {16 \left (1+\frac {3 e^2}{16}\right ) x \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{(-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}-\frac {8 x^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{(-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx}{8-e^2}+\frac {\left (2 e^2\right ) \int \left (-\frac {4 e^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{e^2-2 x}+\frac {8 \left (1+\frac {e^2}{8}\right ) x \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{e^2-2 x}-\frac {2 x^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{e^2-2 x}-\frac {4 e^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}+\frac {16 \left (1+\frac {3 e^2}{16}\right ) x \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}-\frac {8 x^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx}{8-e^2} \\ & = 2 \int x \log ^2\left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right ) \, dx-\frac {16 \int \frac {x^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{-4+x} \, dx}{8-e^2}-\frac {64 \int \frac {x^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{(-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2}-\frac {\left (4 e^2\right ) \int \frac {x^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{e^2-2 x} \, dx}{8-e^2}-\frac {\left (16 e^2\right ) \int \frac {x^2 \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2}-\frac {\left (32 e^2\right ) \int \frac {\log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{-4+x} \, dx}{8-e^2}-\frac {\left (32 e^2\right ) \int \frac {\log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{(-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2}-\frac {\left (8 e^4\right ) \int \frac {\log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{e^2-2 x} \, dx}{8-e^2}-\frac {\left (8 e^4\right ) \int \frac {\log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2}+\frac {\left (8 \left (8+e^2\right )\right ) \int \frac {x \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{-4+x} \, dx}{8-e^2}+\frac {\left (2 e^2 \left (8+e^2\right )\right ) \int \frac {x \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{e^2-2 x} \, dx}{8-e^2}+\frac {\left (8 \left (16+3 e^2\right )\right ) \int \frac {x \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{(-4+x) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2}+\frac {\left (2 e^2 \left (16+3 e^2\right )\right ) \int \frac {x \log \left (\frac {5}{x \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )}\right )}{\left (e^2-2 x\right ) \log \left (-\left (\left (e^2-2 x\right ) (-4+x)^2 x\right )\right )} \, dx}{8-e^2} \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [F]

\[ \int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx=\int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx \]

[In]

Integrate[((-32*x^2 + 16*x^3 + E^2*(8*x - 6*x^2) + (-16*x^2 + 4*x^3 + E^2*(8*x - 2*x^2))*Log[32*x^2 - 16*x^3 +
2*x^4 + E^2*(-16*x + 8*x^2 - x^3)])*Log[5/(x*Log[32*x^2 - 16*x^3 + 2*x^4 + E^2*(-16*x + 8*x^2 - x^3)])] + (16
*x^2 - 4*x^3 + E^2*(-8*x + 2*x^2))*Log[32*x^2 - 16*x^3 + 2*x^4 + E^2*(-16*x + 8*x^2 - x^3)]*Log[5/(x*Log[32*x^
2 - 16*x^3 + 2*x^4 + E^2*(-16*x + 8*x^2 - x^3)])]^2)/((E^2*(-4 + x) + 8*x - 2*x^2)*Log[32*x^2 - 16*x^3 + 2*x^4
+ E^2*(-16*x + 8*x^2 - x^3)]),x]

[Out]

Integrate[((-32*x^2 + 16*x^3 + E^2*(8*x - 6*x^2) + (-16*x^2 + 4*x^3 + E^2*(8*x - 2*x^2))*Log[32*x^2 - 16*x^3 +
2*x^4 + E^2*(-16*x + 8*x^2 - x^3)])*Log[5/(x*Log[32*x^2 - 16*x^3 + 2*x^4 + E^2*(-16*x + 8*x^2 - x^3)])] + (16
*x^2 - 4*x^3 + E^2*(-8*x + 2*x^2))*Log[32*x^2 - 16*x^3 + 2*x^4 + E^2*(-16*x + 8*x^2 - x^3)]*Log[5/(x*Log[32*x^
2 - 16*x^3 + 2*x^4 + E^2*(-16*x + 8*x^2 - x^3)])]^2)/((E^2*(-4 + x) + 8*x - 2*x^2)*Log[32*x^2 - 16*x^3 + 2*x^4
+ E^2*(-16*x + 8*x^2 - x^3)]), x]

Maple [A] (verified)

Time = 806.56 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.48

method	result	size
parallelrisch	\(x^{2} {\ln \left (\frac {5}{x \ln \left (\left (-x^{3}+8 x^{2}-16 x \right ) {\mathrm e}^{2}+2 x^{4}-16 x^{3}+32 x^{2}\right )}\right )}^{2}\)	\(49\)

[In]

int((((2*x^2-8*x)*exp(2)-4*x^3+16*x^2)*ln((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2)*ln(5/x/ln((-x^3+8*x^2-
16*x)*exp(2)+2*x^4-16*x^3+32*x^2))^2+(((-2*x^2+8*x)*exp(2)+4*x^3-16*x^2)*ln((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*
x^3+32*x^2)+(-6*x^2+8*x)*exp(2)+16*x^3-32*x^2)*ln(5/x/ln((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2)))/((x-4
)*exp(2)-2*x^2+8*x)/ln((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2),x,method=_RETURNVERBOSE)

[Out]

x^2*ln(5/x/ln((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2))^2

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.42 \[ \int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx=x^{2} \log \left (\frac {5}{x \log \left (2 \, x^{4} - 16 \, x^{3} + 32 \, x^{2} - {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{2}\right )}\right )^{2} \]

[In]

integrate((((2*x^2-8*x)*exp(2)-4*x^3+16*x^2)*log((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2)*log(5/x/log((-x
^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2))^2+(((-2*x^2+8*x)*exp(2)+4*x^3-16*x^2)*log((-x^3+8*x^2-16*x)*exp(2)
+2*x^4-16*x^3+32*x^2)+(-6*x^2+8*x)*exp(2)+16*x^3-32*x^2)*log(5/x/log((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*
x^2)))/((x-4)*exp(2)-2*x^2+8*x)/log((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2),x, algorithm="fricas")

[Out]

x^2*log(5/(x*log(2*x^4 - 16*x^3 + 32*x^2 - (x^3 - 8*x^2 + 16*x)*e^2)))^2

Sympy [A] (verification not implemented)

Time = 1.15 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.24 \[ \int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx=x^{2} \log {\left (\frac {5}{x \log {\left (2 x^{4} - 16 x^{3} + 32 x^{2} + \left (- x^{3} + 8 x^{2} - 16 x\right ) e^{2} \right )}} \right )}^{2} \]

[In]

integrate((((2*x**2-8*x)*exp(2)-4*x**3+16*x**2)*ln((-x**3+8*x**2-16*x)*exp(2)+2*x**4-16*x**3+32*x**2)*ln(5/x/l
n((-x**3+8*x**2-16*x)*exp(2)+2*x**4-16*x**3+32*x**2))**2+(((-2*x**2+8*x)*exp(2)+4*x**3-16*x**2)*ln((-x**3+8*x*
*2-16*x)*exp(2)+2*x**4-16*x**3+32*x**2)+(-6*x**2+8*x)*exp(2)+16*x**3-32*x**2)*ln(5/x/ln((-x**3+8*x**2-16*x)*ex
p(2)+2*x**4-16*x**3+32*x**2)))/((x-4)*exp(2)-2*x**2+8*x)/ln((-x**3+8*x**2-16*x)*exp(2)+2*x**4-16*x**3+32*x**2)
,x)

[Out]

x**2*log(5/(x*log(2*x**4 - 16*x**3 + 32*x**2 + (-x**3 + 8*x**2 - 16*x)*exp(2))))**2

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 86 vs. \(2 (30) = 60\).

Time = 0.36 (sec) , antiderivative size = 86, normalized size of antiderivative = 2.61 \[ \int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx=x^{2} \log \left (5\right )^{2} - 2 \, x^{2} \log \left (5\right ) \log \left (x\right ) + x^{2} \log \left (x\right )^{2} + x^{2} \log \left (\log \left (2 \, x - e^{2}\right ) + 2 \, \log \left (x - 4\right ) + \log \left (x\right )\right )^{2} - 2 \, {\left (x^{2} \log \left (5\right ) - x^{2} \log \left (x\right )\right )} \log \left (\log \left (2 \, x - e^{2}\right ) + 2 \, \log \left (x - 4\right ) + \log \left (x\right )\right ) \]

[In]

integrate((((2*x^2-8*x)*exp(2)-4*x^3+16*x^2)*log((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2)*log(5/x/log((-x
^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2))^2+(((-2*x^2+8*x)*exp(2)+4*x^3-16*x^2)*log((-x^3+8*x^2-16*x)*exp(2)
+2*x^4-16*x^3+32*x^2)+(-6*x^2+8*x)*exp(2)+16*x^3-32*x^2)*log(5/x/log((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*
x^2)))/((x-4)*exp(2)-2*x^2+8*x)/log((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2),x, algorithm="maxima")

[Out]

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

Giac [F]

\[ \int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx=\int { \frac {2 \, {\left ({\left (2 \, x^{3} - 8 \, x^{2} - {\left (x^{2} - 4 \, x\right )} e^{2}\right )} \log \left (2 \, x^{4} - 16 \, x^{3} + 32 \, x^{2} - {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{2}\right ) \log \left (\frac {5}{x \log \left (2 \, x^{4} - 16 \, x^{3} + 32 \, x^{2} - {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{2}\right )}\right )^{2} - {\left (8 \, x^{3} - 16 \, x^{2} - {\left (3 \, x^{2} - 4 \, x\right )} e^{2} + {\left (2 \, x^{3} - 8 \, x^{2} - {\left (x^{2} - 4 \, x\right )} e^{2}\right )} \log \left (2 \, x^{4} - 16 \, x^{3} + 32 \, x^{2} - {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{2}\right )\right )} \log \left (\frac {5}{x \log \left (2 \, x^{4} - 16 \, x^{3} + 32 \, x^{2} - {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{2}\right )}\right )\right )}}{{\left (2 \, x^{2} - {\left (x - 4\right )} e^{2} - 8 \, x\right )} \log \left (2 \, x^{4} - 16 \, x^{3} + 32 \, x^{2} - {\left (x^{3} - 8 \, x^{2} + 16 \, x\right )} e^{2}\right )} \,d x } \]

[In]

integrate((((2*x^2-8*x)*exp(2)-4*x^3+16*x^2)*log((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2)*log(5/x/log((-x
^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2))^2+(((-2*x^2+8*x)*exp(2)+4*x^3-16*x^2)*log((-x^3+8*x^2-16*x)*exp(2)
+2*x^4-16*x^3+32*x^2)+(-6*x^2+8*x)*exp(2)+16*x^3-32*x^2)*log(5/x/log((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*
x^2)))/((x-4)*exp(2)-2*x^2+8*x)/log((-x^3+8*x^2-16*x)*exp(2)+2*x^4-16*x^3+32*x^2),x, algorithm="giac")

[Out]

integrate(2*((2*x^3 - 8*x^2 - (x^2 - 4*x)*e^2)*log(2*x^4 - 16*x^3 + 32*x^2 - (x^3 - 8*x^2 + 16*x)*e^2)*log(5/(
x*log(2*x^4 - 16*x^3 + 32*x^2 - (x^3 - 8*x^2 + 16*x)*e^2)))^2 - (8*x^3 - 16*x^2 - (3*x^2 - 4*x)*e^2 + (2*x^3 -
8*x^2 - (x^2 - 4*x)*e^2)*log(2*x^4 - 16*x^3 + 32*x^2 - (x^3 - 8*x^2 + 16*x)*e^2))*log(5/(x*log(2*x^4 - 16*x^3
+ 32*x^2 - (x^3 - 8*x^2 + 16*x)*e^2))))/((2*x^2 - (x - 4)*e^2 - 8*x)*log(2*x^4 - 16*x^3 + 32*x^2 - (x^3 - 8*x
^2 + 16*x)*e^2)), x)

Mupad [B] (verification not implemented)

Time = 10.41 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.42 \[ \int \frac {\left (-32 x^2+16 x^3+e^2 \left (8 x-6 x^2\right )+\left (-16 x^2+4 x^3+e^2 \left (8 x-2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )\right ) \log \left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )+\left (16 x^2-4 x^3+e^2 \left (-8 x+2 x^2\right )\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right ) \log ^2\left (\frac {5}{x \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )}\right )}{\left (e^2 (-4+x)+8 x-2 x^2\right ) \log \left (32 x^2-16 x^3+2 x^4+e^2 \left (-16 x+8 x^2-x^3\right )\right )} \, dx=x^2\,{\ln \left (\frac {5}{x\,\ln \left (32\,x^2-{\mathrm {e}}^2\,\left (x^3-8\,x^2+16\,x\right )-16\,x^3+2\,x^4\right )}\right )}^2 \]

[In]

int((log(5/(x*log(32*x^2 - exp(2)*(16*x - 8*x^2 + x^3) - 16*x^3 + 2*x^4)))*(exp(2)*(8*x - 6*x^2) - 32*x^2 + 16
*x^3 + log(32*x^2 - exp(2)*(16*x - 8*x^2 + x^3) - 16*x^3 + 2*x^4)*(exp(2)*(8*x - 2*x^2) - 16*x^2 + 4*x^3)) - l
og(32*x^2 - exp(2)*(16*x - 8*x^2 + x^3) - 16*x^3 + 2*x^4)*log(5/(x*log(32*x^2 - exp(2)*(16*x - 8*x^2 + x^3) -
16*x^3 + 2*x^4)))^2*(exp(2)*(8*x - 2*x^2) - 16*x^2 + 4*x^3))/(log(32*x^2 - exp(2)*(16*x - 8*x^2 + x^3) - 16*x^
3 + 2*x^4)*(8*x + exp(2)*(x - 4) - 2*x^2)),x)

[Out]

x^2*log(5/(x*log(32*x^2 - exp(2)*(16*x - 8*x^2 + x^3) - 16*x^3 + 2*x^4)))^2