\(\int \frac {(96 x^2-3 x^3+e^x (-32 x^3+x^4)) \log (e^{-x} (-3+e^x x))+(-1728 x+54 x^2+e^x (-576 x+18 x^2)+(54 x-18 e^x x^2) \log (e^{-x} (-3+e^x x))) \log (-\frac {16 \log (e^{-x} (-3+e^x x))}{-32+x})+(-864+27 x+e^x (288 x-9 x^2)) \log (e^{-x} (-3+e^x x)) \log ^2(-\frac {16 \log (e^{-x} (-3+e^x x))}{-32+x})}{(96 x^2-3 x^3+e^x (-32 x^3+x^4)) \log (e^{-x} (-3+e^x x))} \, dx\) [1798]

Optimal result

Integrand size = 212, antiderivative size = 30 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=x+\frac {9 \log ^2\left (\frac {\log \left (-3 e^{-x}+x\right )}{2-\frac {x}{16}}\right )}{x} \]

[Out]

x+9*ln(ln(x-3/exp(x))/(2-1/16*x))^2/x

Rubi [F]

\[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx \]

[In]

Int[((96*x^2 - 3*x^3 + E^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x] + (-1728*x + 54*x^2 + E^x*(-576*x + 18*x^2)
+ (54*x - 18*E^x*x^2)*Log[(-3 + E^x*x)/E^x])*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + x)] + (-864 + 27*x + E^x*(
288*x - 9*x^2))*Log[(-3 + E^x*x)/E^x]*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + x)]^2)/((96*x^2 - 3*x^3 + E^x*(-3
2*x^3 + x^4))*Log[(-3 + E^x*x)/E^x]),x]

[Out]

x - (9*Defer[Int][Log[(-16*Log[-3/E^x + x])/(-32 + x)]/(-32 + x), x])/16 + (9*Defer[Int][Log[(-16*Log[-3/E^x +
x])/(-32 + x)]/x, x])/16 + 18*Defer[Int][Log[(-16*Log[-3/E^x + x])/(-32 + x)]/(x^2*Log[-3/E^x + x]), x] + 54*
Defer[Int][Log[(-16*Log[-3/E^x + x])/(-32 + x)]/(x^2*(-3 + E^x*x)*Log[-3/E^x + x]), x] + 54*Defer[Int][Log[(-1
6*Log[-3/E^x + x])/(-32 + x)]/(x*(-3 + E^x*x)*Log[-3/E^x + x]), x] - 9*Defer[Int][Log[(-16*Log[-3/E^x + x])/(-
32 + x)]^2/x^2, x]

Rubi steps \begin{align*} \text {integral}& = \int \left (1-\frac {18 \left (-\left (\left (3+e^x\right ) (-32+x)\right )+\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}-\frac {9 \log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2}\right ) \, dx \\ & = x-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx-18 \int \frac {\left (-\left (\left (3+e^x\right ) (-32+x)\right )+\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx-18 \int \left (-\frac {3 (1+x) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) x^2 \log \left (-3 e^{-x}+x\right )}\right ) \, dx \\ & = x-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx-18 \int \frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {(1+x) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx-18 \int \left (\frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{1024 (-32+x) \log \left (-3 e^{-x}+x\right )}-\frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{32 x^2 \log \left (-3 e^{-x}+x\right )}-\frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{1024 x \log \left (-3 e^{-x}+x\right )}\right ) \, dx+54 \int \left (\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}\right ) \, dx \\ & = x-\frac {9}{512} \int \frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{512} \int \frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{16} \int \frac {\left (32-x+x \log \left (-3 e^{-x}+x\right )\right ) \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \left (\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )-\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{\log \left (-3 e^{-x}+x\right )}+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {9}{512} \int \left (\frac {x \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x}+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}-\frac {x \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}\right ) \, dx+\frac {9}{16} \int \left (\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x}+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )}-\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \log \left (-3 e^{-x}+x\right )}\right ) \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right ) \, dx-\frac {9}{512} \int \frac {x \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx-\frac {9}{512} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{\log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{512} \int \frac {x \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} x \log \left (\frac {16 \log \left (-3 e^{-x}+x\right )}{32-x}\right )-\frac {9}{512} \int \frac {x \left (\frac {3-e^x x}{-32+x}+\frac {3+e^x}{\log \left (-3 e^{-x}+x\right )}\right )}{-3+e^x x} \, dx-\frac {9}{512} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{\log \left (-3 e^{-x}+x\right )} \, dx-\frac {9}{512} \int \left (\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x}\right ) \, dx+\frac {9}{512} \int \left (\frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{\log \left (-3 e^{-x}+x\right )}+\frac {32 \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}\right ) \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} x \log \left (\frac {16 \log \left (-3 e^{-x}+x\right )}{32-x}\right )-\frac {9}{512} \int \left (\frac {3 (1+x)}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {-32+x-x \log \left (-3 e^{-x}+x\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {9}{512} \int \log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right ) \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \frac {x \left (\frac {3-e^x x}{-32+x}+\frac {3+e^x}{\log \left (-3 e^{-x}+x\right )}\right )}{-3+e^x x} \, dx-\frac {9}{512} \int \frac {-32+x-x \log \left (-3 e^{-x}+x\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {27}{512} \int \frac {1+x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x-\frac {9}{512} \int \left (-\frac {x}{-32+x}+\frac {1}{\log \left (-3 e^{-x}+x\right )}\right ) \, dx+\frac {9}{512} \int \left (\frac {3 (1+x)}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {-32+x-x \log \left (-3 e^{-x}+x\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {27}{512} \int \left (\frac {1}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \frac {x}{-32+x} \, dx-\frac {9}{512} \int \frac {1}{\log \left (-3 e^{-x}+x\right )} \, dx+\frac {9}{512} \int \frac {-32+x-x \log \left (-3 e^{-x}+x\right )}{(-32+x) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {27}{512} \int \frac {1}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {27}{512} \int \frac {x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+\frac {27}{512} \int \frac {1+x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x+\frac {9}{512} \int \left (1+\frac {32}{-32+x}\right ) \, dx+\frac {9}{512} \int \left (-\frac {x}{-32+x}+\frac {1}{\log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {9}{512} \int \frac {1}{\log \left (-3 e^{-x}+x\right )} \, dx+\frac {27}{512} \int \left (\frac {1}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}+\frac {x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )}\right ) \, dx-\frac {27}{512} \int \frac {1}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {27}{512} \int \frac {x}{\left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = \frac {521 x}{512}+\frac {9}{16} \log (32-x)-\frac {9}{512} \int \frac {x}{-32+x} \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = \frac {521 x}{512}+\frac {9}{16} \log (32-x)-\frac {9}{512} \int \left (1+\frac {32}{-32+x}\right ) \, dx-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ & = x-\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{-32+x} \, dx+\frac {9}{16} \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x} \, dx-9 \int \frac {\log ^2\left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2} \, dx+18 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x^2 \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx+54 \int \frac {\log \left (-\frac {16 \log \left (-3 e^{-x}+x\right )}{-32+x}\right )}{x \left (-3+e^x x\right ) \log \left (-3 e^{-x}+x\right )} \, dx \\ \end{align*}

Mathematica [F]

\[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx \]

[In]

Integrate[((96*x^2 - 3*x^3 + E^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x] + (-1728*x + 54*x^2 + E^x*(-576*x + 18
*x^2) + (54*x - 18*E^x*x^2)*Log[(-3 + E^x*x)/E^x])*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + x)] + (-864 + 27*x +
E^x*(288*x - 9*x^2))*Log[(-3 + E^x*x)/E^x]*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + x)]^2)/((96*x^2 - 3*x^3 + E
^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x]),x]

[Out]

Integrate[((96*x^2 - 3*x^3 + E^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x] + (-1728*x + 54*x^2 + E^x*(-576*x + 18
*x^2) + (54*x - 18*E^x*x^2)*Log[(-3 + E^x*x)/E^x])*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + x)] + (-864 + 27*x +
E^x*(288*x - 9*x^2))*Log[(-3 + E^x*x)/E^x]*Log[(-16*Log[(-3 + E^x*x)/E^x])/(-32 + x)]^2)/((96*x^2 - 3*x^3 + E
^x*(-32*x^3 + x^4))*Log[(-3 + E^x*x)/E^x]), x]

Maple [A] (verified)

Time = 13.19 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.30

method	result	size
parallelrisch	\(-\frac {-384 x^{2}-3456 {\ln \left (-\frac {16 \ln \left (\left ({\mathrm e}^{x} x -3\right ) {\mathrm e}^{-x}\right )}{x -32}\right )}^{2}-6144 x}{384 x}\)	\(39\)

[In]

int((((-9*x^2+288*x)*exp(x)+27*x-864)*ln((exp(x)*x-3)/exp(x))*ln(-16*ln((exp(x)*x-3)/exp(x))/(x-32))^2+((-18*e
xp(x)*x^2+54*x)*ln((exp(x)*x-3)/exp(x))+(18*x^2-576*x)*exp(x)+54*x^2-1728*x)*ln(-16*ln((exp(x)*x-3)/exp(x))/(x
-32))+((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)*ln((exp(x)*x-3)/exp(x)))/((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)/ln((exp(x
)*x-3)/exp(x)),x,method=_RETURNVERBOSE)

[Out]

-1/384*(-384*x^2-3456*ln(-16*ln((exp(x)*x-3)/exp(x))/(x-32))^2-6144*x)/x

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.07 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\frac {x^{2} + 9 \, \log \left (-\frac {16 \, \log \left ({\left (x e^{x} - 3\right )} e^{\left (-x\right )}\right )}{x - 32}\right )^{2}}{x} \]

[In]

integrate((((-9*x^2+288*x)*exp(x)+27*x-864)*log((exp(x)*x-3)/exp(x))*log(-16*log((exp(x)*x-3)/exp(x))/(x-32))^
2+((-18*exp(x)*x^2+54*x)*log((exp(x)*x-3)/exp(x))+(18*x^2-576*x)*exp(x)+54*x^2-1728*x)*log(-16*log((exp(x)*x-3
)/exp(x))/(x-32))+((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)*log((exp(x)*x-3)/exp(x)))/((x^4-32*x^3)*exp(x)-3*x^3+96*x
^2)/log((exp(x)*x-3)/exp(x)),x, algorithm="fricas")

[Out]

(x^2 + 9*log(-16*log((x*e^x - 3)*e^(-x))/(x - 32))^2)/x

Sympy [A] (verification not implemented)

Time = 0.78 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=x + \frac {9 \log {\left (- \frac {16 \log {\left (\left (x e^{x} - 3\right ) e^{- x} \right )}}{x - 32} \right )}^{2}}{x} \]

[In]

integrate((((-9*x**2+288*x)*exp(x)+27*x-864)*ln((exp(x)*x-3)/exp(x))*ln(-16*ln((exp(x)*x-3)/exp(x))/(x-32))**2
+((-18*exp(x)*x**2+54*x)*ln((exp(x)*x-3)/exp(x))+(18*x**2-576*x)*exp(x)+54*x**2-1728*x)*ln(-16*ln((exp(x)*x-3)
/exp(x))/(x-32))+((x**4-32*x**3)*exp(x)-3*x**3+96*x**2)*ln((exp(x)*x-3)/exp(x)))/((x**4-32*x**3)*exp(x)-3*x**3
+96*x**2)/ln((exp(x)*x-3)/exp(x)),x)

[Out]

x + 9*log(-16*log((x*exp(x) - 3)*exp(-x))/(x - 32))**2/x

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (26) = 52\).

Time = 0.37 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.37 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=\frac {x^{2} + 144 \, \log \left (2\right )^{2} + 18 \, {\left (4 \, \log \left (2\right ) - \log \left (x - 32\right )\right )} \log \left (x - \log \left (x e^{x} - 3\right )\right ) + 9 \, \log \left (x - \log \left (x e^{x} - 3\right )\right )^{2} - 72 \, \log \left (2\right ) \log \left (x - 32\right ) + 9 \, \log \left (x - 32\right )^{2}}{x} \]

[In]

integrate((((-9*x^2+288*x)*exp(x)+27*x-864)*log((exp(x)*x-3)/exp(x))*log(-16*log((exp(x)*x-3)/exp(x))/(x-32))^
2+((-18*exp(x)*x^2+54*x)*log((exp(x)*x-3)/exp(x))+(18*x^2-576*x)*exp(x)+54*x^2-1728*x)*log(-16*log((exp(x)*x-3
)/exp(x))/(x-32))+((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)*log((exp(x)*x-3)/exp(x)))/((x^4-32*x^3)*exp(x)-3*x^3+96*x
^2)/log((exp(x)*x-3)/exp(x)),x, algorithm="maxima")

[Out]

(x^2 + 144*log(2)^2 + 18*(4*log(2) - log(x - 32))*log(x - log(x*e^x - 3)) + 9*log(x - log(x*e^x - 3))^2 - 72*l
og(2)*log(x - 32) + 9*log(x - 32)^2)/x

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 426 vs. \(2 (26) = 52\).

Time = 3.87 (sec) , antiderivative size = 426, normalized size of antiderivative = 14.20 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=-\frac {9 \, \pi ^{2} \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) \mathrm {sgn}\left (x - 32\right ) \mathrm {sgn}\left (\log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )\right ) + 9 \, \pi ^{2} \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) \mathrm {sgn}\left (x - 32\right ) + 27 \, \pi ^{2} \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) \mathrm {sgn}\left (\log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )\right ) - 18 \, \pi \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right ) \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) \mathrm {sgn}\left (\log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )\right ) + 27 \, \pi ^{2} \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) - 18 \, \pi \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right ) \mathrm {sgn}\left (-8 \, \pi + 8 \, \pi \mathrm {sgn}\left (x e^{x} - 3\right )\right ) + 27 \, \pi ^{2} \mathrm {sgn}\left (x - 32\right ) - 18 \, \pi \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right ) \mathrm {sgn}\left (x - 32\right ) + 9 \, \pi ^{2} \mathrm {sgn}\left (\log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )\right ) + 54 \, \pi ^{2} - 2 \, x^{2} - 54 \, \pi \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right ) + 18 \, \arctan \left (-\frac {\pi - \pi \mathrm {sgn}\left (x e^{x} - 3\right )}{2 \, \log \left ({\left | x e^{x} - 3 \right |} e^{\left (-x\right )}\right )}\right )^{2} - 18 \, \log \left (16 \, {\left | \log \left ({\left (x e^{x} - 3\right )} e^{\left (-x\right )}\right ) \right |}\right )^{2} + 36 \, \log \left (16 \, {\left | \log \left ({\left (x e^{x} - 3\right )} e^{\left (-x\right )}\right ) \right |}\right ) \log \left ({\left | x - 32 \right |}\right ) - 18 \, \log \left ({\left | x - 32 \right |}\right )^{2}}{2 \, x} \]

[In]

integrate((((-9*x^2+288*x)*exp(x)+27*x-864)*log((exp(x)*x-3)/exp(x))*log(-16*log((exp(x)*x-3)/exp(x))/(x-32))^
2+((-18*exp(x)*x^2+54*x)*log((exp(x)*x-3)/exp(x))+(18*x^2-576*x)*exp(x)+54*x^2-1728*x)*log(-16*log((exp(x)*x-3
)/exp(x))/(x-32))+((x^4-32*x^3)*exp(x)-3*x^3+96*x^2)*log((exp(x)*x-3)/exp(x)))/((x^4-32*x^3)*exp(x)-3*x^3+96*x
^2)/log((exp(x)*x-3)/exp(x)),x, algorithm="giac")

[Out]

-1/2*(9*pi^2*sgn(-8*pi + 8*pi*sgn(x*e^x - 3))*sgn(x - 32)*sgn(log(abs(x*e^x - 3)*e^(-x))) + 9*pi^2*sgn(-8*pi +
8*pi*sgn(x*e^x - 3))*sgn(x - 32) + 27*pi^2*sgn(-8*pi + 8*pi*sgn(x*e^x - 3))*sgn(log(abs(x*e^x - 3)*e^(-x))) -
18*pi*arctan(-1/2*(pi - pi*sgn(x*e^x - 3))/log(abs(x*e^x - 3)*e^(-x)))*sgn(-8*pi + 8*pi*sgn(x*e^x - 3))*sgn(l
og(abs(x*e^x - 3)*e^(-x))) + 27*pi^2*sgn(-8*pi + 8*pi*sgn(x*e^x - 3)) - 18*pi*arctan(-1/2*(pi - pi*sgn(x*e^x -
3))/log(abs(x*e^x - 3)*e^(-x)))*sgn(-8*pi + 8*pi*sgn(x*e^x - 3)) + 27*pi^2*sgn(x - 32) - 18*pi*arctan(-1/2*(p
i - pi*sgn(x*e^x - 3))/log(abs(x*e^x - 3)*e^(-x)))*sgn(x - 32) + 9*pi^2*sgn(log(abs(x*e^x - 3)*e^(-x))) + 54*p
i^2 - 2*x^2 - 54*pi*arctan(-1/2*(pi - pi*sgn(x*e^x - 3))/log(abs(x*e^x - 3)*e^(-x))) + 18*arctan(-1/2*(pi - pi
*sgn(x*e^x - 3))/log(abs(x*e^x - 3)*e^(-x)))^2 - 18*log(16*abs(log((x*e^x - 3)*e^(-x))))^2 + 36*log(16*abs(log
((x*e^x - 3)*e^(-x))))*log(abs(x - 32)) - 18*log(abs(x - 32))^2)/x

Mupad [B] (verification not implemented)

Time = 9.66 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.87 \[ \int \frac {\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )+\left (-1728 x+54 x^2+e^x \left (-576 x+18 x^2\right )+\left (54 x-18 e^x x^2\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )\right ) \log \left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )+\left (-864+27 x+e^x \left (288 x-9 x^2\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right ) \log ^2\left (-\frac {16 \log \left (e^{-x} \left (-3+e^x x\right )\right )}{-32+x}\right )}{\left (96 x^2-3 x^3+e^x \left (-32 x^3+x^4\right )\right ) \log \left (e^{-x} \left (-3+e^x x\right )\right )} \, dx=x+\frac {9\,{\ln \left (-\frac {16\,\ln \left (x-3\,{\mathrm {e}}^{-x}\right )}{x-32}\right )}^2}{x} \]

[In]

int((log(exp(-x)*(x*exp(x) - 3))*(exp(x)*(32*x^3 - x^4) - 96*x^2 + 3*x^3) + log(-(16*log(exp(-x)*(x*exp(x) - 3
)))/(x - 32))*(1728*x + exp(x)*(576*x - 18*x^2) - log(exp(-x)*(x*exp(x) - 3))*(54*x - 18*x^2*exp(x)) - 54*x^2)
- log(exp(-x)*(x*exp(x) - 3))*log(-(16*log(exp(-x)*(x*exp(x) - 3)))/(x - 32))^2*(27*x + exp(x)*(288*x - 9*x^2
) - 864))/(log(exp(-x)*(x*exp(x) - 3))*(exp(x)*(32*x^3 - x^4) - 96*x^2 + 3*x^3)),x)

[Out]

x + (9*log(-(16*log(x - 3*exp(-x)))/(x - 32))^2)/x