Integrand size = 281, antiderivative size = 29 \[ \int \frac {e^x (-4+2 x) \log (-2+x)+\left (-e^x x+e^x (-2+x) \log (-2+x)\right ) \log \left (x^2\right )+e^x \left (2 x^2-x^3\right ) \log ^2\left (x^2\right )+\left (e^x (-2+x) \log (-2+x) \log \left (x^2\right )+e^x \left (-2 x^2+x^3\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )+\left (e^x \left (2-3 x+x^2\right ) \log (-2+x) \log \left (x^2\right )+e^x \left (2 x^2-3 x^3+x^4\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )}\right )}{\left (\left (-2 x^2+x^3\right ) \log (-2+x) \log \left (x^2\right )+\left (-2 x^4+x^5\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )} \, dx=\frac {e^x \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )}{x} \]
Time = 0.48 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {e^x (-4+2 x) \log (-2+x)+\left (-e^x x+e^x (-2+x) \log (-2+x)\right ) \log \left (x^2\right )+e^x \left (2 x^2-x^3\right ) \log ^2\left (x^2\right )+\left (e^x (-2+x) \log (-2+x) \log \left (x^2\right )+e^x \left (-2 x^2+x^3\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )+\left (e^x \left (2-3 x+x^2\right ) \log (-2+x) \log \left (x^2\right )+e^x \left (2 x^2-3 x^3+x^4\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )}\right )}{\left (\left (-2 x^2+x^3\right ) \log (-2+x) \log \left (x^2\right )+\left (-2 x^4+x^5\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )} \, dx=\frac {e^x \log \left (\frac {x}{\log \left (x+\frac {\log (-2+x)}{x \log \left (x^2\right )}\right )}\right )}{x} \]
Integrate[(E^x*(-4 + 2*x)*Log[-2 + x] + (-(E^x*x) + E^x*(-2 + x)*Log[-2 + x])*Log[x^2] + E^x*(2*x^2 - x^3)*Log[x^2]^2 + (E^x*(-2 + x)*Log[-2 + x]*Lo g[x^2] + E^x*(-2*x^2 + x^3)*Log[x^2]^2)*Log[(Log[-2 + x] + x^2*Log[x^2])/( x*Log[x^2])] + (E^x*(2 - 3*x + x^2)*Log[-2 + x]*Log[x^2] + E^x*(2*x^2 - 3* x^3 + x^4)*Log[x^2]^2)*Log[(Log[-2 + x] + x^2*Log[x^2])/(x*Log[x^2])]*Log[ x/Log[(Log[-2 + x] + x^2*Log[x^2])/(x*Log[x^2])]])/(((-2*x^2 + x^3)*Log[-2 + x]*Log[x^2] + (-2*x^4 + x^5)*Log[x^2]^2)*Log[(Log[-2 + x] + x^2*Log[x^2 ])/(x*Log[x^2])]),x]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {\left (e^x (x-2) \log (x-2)-e^x x\right ) \log \left (x^2\right )+e^x \left (2 x^2-x^3\right ) \log ^2\left (x^2\right )+\left (e^x (x-2) \log (x-2) \log \left (x^2\right )+e^x \left (x^3-2 x^2\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {x^2 \log \left (x^2\right )+\log (x-2)}{x \log \left (x^2\right )}\right )+\left (e^x \left (x^2-3 x+2\right ) \log (x-2) \log \left (x^2\right )+e^x \left (x^4-3 x^3+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {x^2 \log \left (x^2\right )+\log (x-2)}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (\frac {x^2 \log \left (x^2\right )+\log (x-2)}{x \log \left (x^2\right )}\right )}\right )+e^x (2 x-4) \log (x-2)}{\left (\left (x^3-2 x^2\right ) \log (x-2) \log \left (x^2\right )+\left (x^5-2 x^4\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {x^2 \log \left (x^2\right )+\log (x-2)}{x \log \left (x^2\right )}\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-\left (e^x (x-2) \log (x-2)-e^x x\right ) \log \left (x^2\right )-e^x \left (2 x^2-x^3\right ) \log ^2\left (x^2\right )-\left (e^x (x-2) \log (x-2) \log \left (x^2\right )+e^x \left (x^3-2 x^2\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {x^2 \log \left (x^2\right )+\log (x-2)}{x \log \left (x^2\right )}\right )-\left (e^x \left (x^2-3 x+2\right ) \log (x-2) \log \left (x^2\right )+e^x \left (x^4-3 x^3+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {x^2 \log \left (x^2\right )+\log (x-2)}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (\frac {x^2 \log \left (x^2\right )+\log (x-2)}{x \log \left (x^2\right )}\right )}\right )-e^x (2 x-4) \log (x-2)}{(2-x) x^2 \log \left (x^2\right ) \left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {x^2 \log \left (x^2\right )+\log (x-2)}{x \log \left (x^2\right )}\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^x \left (\log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^4-\log ^2\left (x^2\right ) x^3+\log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) x^3-3 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^3+2 \log ^2\left (x^2\right ) x^2-2 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) x^2+2 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^2+\log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^2+2 \log (x-2) x+\log (x-2) \log \left (x^2\right ) x-\log \left (x^2\right ) x+\log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) x-3 \log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x-4 \log (x-2)-2 \log (x-2) \log \left (x^2\right )-2 \log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )+2 \log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right )\right )}{4 (x-2) \log \left (x^2\right ) \left (\log \left (x^2\right ) x^2+\log (x-2)\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}-\frac {e^x \left (\log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^4-\log ^2\left (x^2\right ) x^3+\log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) x^3-3 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^3+2 \log ^2\left (x^2\right ) x^2-2 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) x^2+2 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^2+\log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^2+2 \log (x-2) x+\log (x-2) \log \left (x^2\right ) x-\log \left (x^2\right ) x+\log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) x-3 \log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x-4 \log (x-2)-2 \log (x-2) \log \left (x^2\right )-2 \log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )+2 \log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right )\right )}{4 x \log \left (x^2\right ) \left (\log \left (x^2\right ) x^2+\log (x-2)\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}-\frac {e^x \left (\log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^4-\log ^2\left (x^2\right ) x^3+\log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) x^3-3 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^3+2 \log ^2\left (x^2\right ) x^2-2 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) x^2+2 \log ^2\left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^2+\log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x^2+2 \log (x-2) x+\log (x-2) \log \left (x^2\right ) x-\log \left (x^2\right ) x+\log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) x-3 \log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right ) x-4 \log (x-2)-2 \log (x-2) \log \left (x^2\right )-2 \log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )+2 \log (x-2) \log \left (x^2\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right ) \log \left (\frac {x}{\log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right )\right )}{2 x^2 \log \left (x^2\right ) \left (\log \left (x^2\right ) x^2+\log (x-2)\right ) \log \left (x+\frac {\log (x-2)}{\log \left (x^2\right ) x}\right )}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^x \left (-x \log \left (x^2\right ) \left ((x-2) x \log \left (x^2\right ) \left (\log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right ) \left ((x-1) \log \left (\frac {x}{\log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}\right )+1\right )-1\right )-1\right )-(x-2) \log (x-2) \left (\log \left (x^2\right ) \left (\log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right ) \left ((x-1) \log \left (\frac {x}{\log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}\right )+1\right )+1\right )+2\right )\right )}{(2-x) x^2 \log \left (x^2\right ) \left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^x \log (x-2)}{x^2 \left (x^2 \log \left (x^2\right )+\log (x-2)\right )}+\frac {2 e^x \log (x-2)}{x^2 \log \left (x^2\right ) \left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}+\frac {e^x \log (x-2)}{x^2 \left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}+\frac {e^x (x-1) \log \left (\frac {x}{\log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}\right )}{x^2}+\frac {e^x \log \left (x^2\right )}{x^2 \log \left (x^2\right )+\log (x-2)}-\frac {e^x \log \left (x^2\right )}{\left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}-\frac {e^x}{(x-2) x \left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {e^x \log (x-2)}{x^2 \left (x^2 \log \left (x^2\right )+\log (x-2)\right )}+\frac {2 e^x \log (x-2)}{x^2 \log \left (x^2\right ) \left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}+\frac {e^x \log (x-2)}{x^2 \left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}+\frac {e^x (x-1) \log \left (\frac {x}{\log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}\right )}{x^2}+\frac {e^x \log \left (x^2\right )}{x^2 \log \left (x^2\right )+\log (x-2)}-\frac {e^x \log \left (x^2\right )}{\left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}-\frac {e^x}{(x-2) x \left (x^2 \log \left (x^2\right )+\log (x-2)\right ) \log \left (\frac {\log (x-2)}{x \log \left (x^2\right )}+x\right )}\right )dx\) |
Int[(E^x*(-4 + 2*x)*Log[-2 + x] + (-(E^x*x) + E^x*(-2 + x)*Log[-2 + x])*Lo g[x^2] + E^x*(2*x^2 - x^3)*Log[x^2]^2 + (E^x*(-2 + x)*Log[-2 + x]*Log[x^2] + E^x*(-2*x^2 + x^3)*Log[x^2]^2)*Log[(Log[-2 + x] + x^2*Log[x^2])/(x*Log[ x^2])] + (E^x*(2 - 3*x + x^2)*Log[-2 + x]*Log[x^2] + E^x*(2*x^2 - 3*x^3 + x^4)*Log[x^2]^2)*Log[(Log[-2 + x] + x^2*Log[x^2])/(x*Log[x^2])]*Log[x/Log[ (Log[-2 + x] + x^2*Log[x^2])/(x*Log[x^2])]])/(((-2*x^2 + x^3)*Log[-2 + x]* Log[x^2] + (-2*x^4 + x^5)*Log[x^2]^2)*Log[(Log[-2 + x] + x^2*Log[x^2])/(x* Log[x^2])]),x]
3.13.63.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 2.78 (sec) , antiderivative size = 22245, normalized size of antiderivative = 767.07
\[\text {output too large to display}\]
int((((x^4-3*x^3+2*x^2)*exp(x)*ln(x^2)^2+(x^2-3*x+2)*exp(x)*ln(-2+x)*ln(x^ 2))*ln((x^2*ln(x^2)+ln(-2+x))/x/ln(x^2))*ln(x/ln((x^2*ln(x^2)+ln(-2+x))/x/ ln(x^2)))+((x^3-2*x^2)*exp(x)*ln(x^2)^2+(-2+x)*exp(x)*ln(-2+x)*ln(x^2))*ln ((x^2*ln(x^2)+ln(-2+x))/x/ln(x^2))+(-x^3+2*x^2)*exp(x)*ln(x^2)^2+((-2+x)*e xp(x)*ln(-2+x)-exp(x)*x)*ln(x^2)+(2*x-4)*exp(x)*ln(-2+x))/((x^5-2*x^4)*ln( x^2)^2+(x^3-2*x^2)*ln(-2+x)*ln(x^2))/ln((x^2*ln(x^2)+ln(-2+x))/x/ln(x^2)), x)
Time = 0.26 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.21 \[ \int \frac {e^x (-4+2 x) \log (-2+x)+\left (-e^x x+e^x (-2+x) \log (-2+x)\right ) \log \left (x^2\right )+e^x \left (2 x^2-x^3\right ) \log ^2\left (x^2\right )+\left (e^x (-2+x) \log (-2+x) \log \left (x^2\right )+e^x \left (-2 x^2+x^3\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )+\left (e^x \left (2-3 x+x^2\right ) \log (-2+x) \log \left (x^2\right )+e^x \left (2 x^2-3 x^3+x^4\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )}\right )}{\left (\left (-2 x^2+x^3\right ) \log (-2+x) \log \left (x^2\right )+\left (-2 x^4+x^5\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )} \, dx=\frac {e^{x} \log \left (\frac {x}{\log \left (\frac {x^{2} \log \left (x^{2}\right ) + \log \left (x - 2\right )}{x \log \left (x^{2}\right )}\right )}\right )}{x} \]
integrate((((x^4-3*x^3+2*x^2)*exp(x)*log(x^2)^2+(x^2-3*x+2)*exp(x)*log(-2+ x)*log(x^2))*log((x^2*log(x^2)+log(-2+x))/x/log(x^2))*log(x/log((x^2*log(x ^2)+log(-2+x))/x/log(x^2)))+((x^3-2*x^2)*exp(x)*log(x^2)^2+(-2+x)*exp(x)*l og(-2+x)*log(x^2))*log((x^2*log(x^2)+log(-2+x))/x/log(x^2))+(-x^3+2*x^2)*e xp(x)*log(x^2)^2+((-2+x)*exp(x)*log(-2+x)-exp(x)*x)*log(x^2)+(2*x-4)*exp(x )*log(-2+x))/((x^5-2*x^4)*log(x^2)^2+(x^3-2*x^2)*log(-2+x)*log(x^2))/log(( x^2*log(x^2)+log(-2+x))/x/log(x^2)),x, algorithm=\
Timed out. \[ \int \frac {e^x (-4+2 x) \log (-2+x)+\left (-e^x x+e^x (-2+x) \log (-2+x)\right ) \log \left (x^2\right )+e^x \left (2 x^2-x^3\right ) \log ^2\left (x^2\right )+\left (e^x (-2+x) \log (-2+x) \log \left (x^2\right )+e^x \left (-2 x^2+x^3\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )+\left (e^x \left (2-3 x+x^2\right ) \log (-2+x) \log \left (x^2\right )+e^x \left (2 x^2-3 x^3+x^4\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )}\right )}{\left (\left (-2 x^2+x^3\right ) \log (-2+x) \log \left (x^2\right )+\left (-2 x^4+x^5\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )} \, dx=\text {Timed out} \]
integrate((((x**4-3*x**3+2*x**2)*exp(x)*ln(x**2)**2+(x**2-3*x+2)*exp(x)*ln (-2+x)*ln(x**2))*ln((x**2*ln(x**2)+ln(-2+x))/x/ln(x**2))*ln(x/ln((x**2*ln( x**2)+ln(-2+x))/x/ln(x**2)))+((x**3-2*x**2)*exp(x)*ln(x**2)**2+(-2+x)*exp( x)*ln(-2+x)*ln(x**2))*ln((x**2*ln(x**2)+ln(-2+x))/x/ln(x**2))+(-x**3+2*x** 2)*exp(x)*ln(x**2)**2+((-2+x)*exp(x)*ln(-2+x)-exp(x)*x)*ln(x**2)+(2*x-4)*e xp(x)*ln(-2+x))/((x**5-2*x**4)*ln(x**2)**2+(x**3-2*x**2)*ln(-2+x)*ln(x**2) )/ln((x**2*ln(x**2)+ln(-2+x))/x/ln(x**2)),x)
Time = 0.42 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.45 \[ \int \frac {e^x (-4+2 x) \log (-2+x)+\left (-e^x x+e^x (-2+x) \log (-2+x)\right ) \log \left (x^2\right )+e^x \left (2 x^2-x^3\right ) \log ^2\left (x^2\right )+\left (e^x (-2+x) \log (-2+x) \log \left (x^2\right )+e^x \left (-2 x^2+x^3\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )+\left (e^x \left (2-3 x+x^2\right ) \log (-2+x) \log \left (x^2\right )+e^x \left (2 x^2-3 x^3+x^4\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )}\right )}{\left (\left (-2 x^2+x^3\right ) \log (-2+x) \log \left (x^2\right )+\left (-2 x^4+x^5\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )} \, dx=\frac {e^{x} \log \left (x\right ) - e^{x} \log \left (-\log \left (2\right ) + \log \left (2 \, x^{2} \log \left (x\right ) + \log \left (x - 2\right )\right ) - \log \left (x\right ) - \log \left (\log \left (x\right )\right )\right )}{x} \]
integrate((((x^4-3*x^3+2*x^2)*exp(x)*log(x^2)^2+(x^2-3*x+2)*exp(x)*log(-2+ x)*log(x^2))*log((x^2*log(x^2)+log(-2+x))/x/log(x^2))*log(x/log((x^2*log(x ^2)+log(-2+x))/x/log(x^2)))+((x^3-2*x^2)*exp(x)*log(x^2)^2+(-2+x)*exp(x)*l og(-2+x)*log(x^2))*log((x^2*log(x^2)+log(-2+x))/x/log(x^2))+(-x^3+2*x^2)*e xp(x)*log(x^2)^2+((-2+x)*exp(x)*log(-2+x)-exp(x)*x)*log(x^2)+(2*x-4)*exp(x )*log(-2+x))/((x^5-2*x^4)*log(x^2)^2+(x^3-2*x^2)*log(-2+x)*log(x^2))/log(( x^2*log(x^2)+log(-2+x))/x/log(x^2)),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 2231 vs. \(2 (28) = 56\).
Time = 7.28 (sec) , antiderivative size = 2231, normalized size of antiderivative = 76.93 \[ \int \frac {e^x (-4+2 x) \log (-2+x)+\left (-e^x x+e^x (-2+x) \log (-2+x)\right ) \log \left (x^2\right )+e^x \left (2 x^2-x^3\right ) \log ^2\left (x^2\right )+\left (e^x (-2+x) \log (-2+x) \log \left (x^2\right )+e^x \left (-2 x^2+x^3\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )+\left (e^x \left (2-3 x+x^2\right ) \log (-2+x) \log \left (x^2\right )+e^x \left (2 x^2-3 x^3+x^4\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )}\right )}{\left (\left (-2 x^2+x^3\right ) \log (-2+x) \log \left (x^2\right )+\left (-2 x^4+x^5\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )} \, dx=\text {Too large to display} \]
integrate((((x^4-3*x^3+2*x^2)*exp(x)*log(x^2)^2+(x^2-3*x+2)*exp(x)*log(-2+ x)*log(x^2))*log((x^2*log(x^2)+log(-2+x))/x/log(x^2))*log(x/log((x^2*log(x ^2)+log(-2+x))/x/log(x^2)))+((x^3-2*x^2)*exp(x)*log(x^2)^2+(-2+x)*exp(x)*l og(-2+x)*log(x^2))*log((x^2*log(x^2)+log(-2+x))/x/log(x^2))+(-x^3+2*x^2)*e xp(x)*log(x^2)^2+((-2+x)*exp(x)*log(-2+x)-exp(x)*x)*log(x^2)+(2*x-4)*exp(x )*log(-2+x))/((x^5-2*x^4)*log(x^2)^2+(x^3-2*x^2)*log(-2+x)*log(x^2))/log(( x^2*log(x^2)+log(-2+x))/x/log(x^2)),x, algorithm=\
-1/2*(e^x*log(-1/2*pi^2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x ^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1 ) + pi*sgn(x))*sgn(x^2*log(x^2) + log(abs(x - 2)))*sgn(log(x^2)) + 1/2*pi^ 2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x))*sgn(x^2 *log(x^2) + log(abs(x - 2))) + 1/2*pi^2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn( x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(x^2*log(x^2) + l og(abs(x - 2)))*sgn(x) + 1/2*pi^2*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1 ) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(-pi + 2*pi*floor(-1/2* sgn(x) + 1) + pi*sgn(x))*sgn(log(x^2)) - 1/2*pi^2*sgn(-pi + 2*pi*floor(-1/ 2*sgn(x) + 1) + pi*sgn(x))*sgn(x)*sgn(log(x^2)) - 1/2*pi^2*sgn(-pi + 4*pi* x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*s gn(-pi + 2*pi*floor(-1/2*sgn(x) + 1) + pi*sgn(x)) - 1/2*pi^2*sgn(-pi + 4*p i*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2)) *sgn(x^2*log(x^2) + log(abs(x - 2))) - pi*arctan(-1/2*(pi - 4*pi*x^2*floor (-1/2*sgn(x) + 1) - 2*pi*x^2*sgn(x) + 2*pi*x^2 - pi*sgn(x - 2))/(x^2*log(x ^2) + log(abs(x - 2))))*sgn(-pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x ^2*sgn(x) - 2*pi*x^2 + pi*sgn(x - 2))*sgn(x^2*log(x^2) + log(abs(x - 2))) + pi*arctan(-(pi - 2*pi*floor(-1/2*sgn(x) + 1) - pi*sgn(x))/log(x^2))*sgn( -pi + 4*pi*x^2*floor(-1/2*sgn(x) + 1) + 2*pi*x^2*sgn(x) - 2*pi*x^2 + pi...
Timed out. \[ \int \frac {e^x (-4+2 x) \log (-2+x)+\left (-e^x x+e^x (-2+x) \log (-2+x)\right ) \log \left (x^2\right )+e^x \left (2 x^2-x^3\right ) \log ^2\left (x^2\right )+\left (e^x (-2+x) \log (-2+x) \log \left (x^2\right )+e^x \left (-2 x^2+x^3\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )+\left (e^x \left (2-3 x+x^2\right ) \log (-2+x) \log \left (x^2\right )+e^x \left (2 x^2-3 x^3+x^4\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right ) \log \left (\frac {x}{\log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )}\right )}{\left (\left (-2 x^2+x^3\right ) \log (-2+x) \log \left (x^2\right )+\left (-2 x^4+x^5\right ) \log ^2\left (x^2\right )\right ) \log \left (\frac {\log (-2+x)+x^2 \log \left (x^2\right )}{x \log \left (x^2\right )}\right )} \, dx=\int -\frac {\ln \left (\frac {x}{\ln \left (\frac {\ln \left (x-2\right )+x^2\,\ln \left (x^2\right )}{x\,\ln \left (x^2\right )}\right )}\right )\,\ln \left (\frac {\ln \left (x-2\right )+x^2\,\ln \left (x^2\right )}{x\,\ln \left (x^2\right )}\right )\,\left ({\mathrm {e}}^x\,\left (x^4-3\,x^3+2\,x^2\right )\,{\ln \left (x^2\right )}^2+\ln \left (x-2\right )\,{\mathrm {e}}^x\,\left (x^2-3\,x+2\right )\,\ln \left (x^2\right )\right )-\ln \left (\frac {\ln \left (x-2\right )+x^2\,\ln \left (x^2\right )}{x\,\ln \left (x^2\right )}\right )\,\left ({\ln \left (x^2\right )}^2\,{\mathrm {e}}^x\,\left (2\,x^2-x^3\right )-\ln \left (x-2\right )\,\ln \left (x^2\right )\,{\mathrm {e}}^x\,\left (x-2\right )\right )-\ln \left (x^2\right )\,\left (x\,{\mathrm {e}}^x-\ln \left (x-2\right )\,{\mathrm {e}}^x\,\left (x-2\right )\right )+{\ln \left (x^2\right )}^2\,{\mathrm {e}}^x\,\left (2\,x^2-x^3\right )+\ln \left (x-2\right )\,{\mathrm {e}}^x\,\left (2\,x-4\right )}{\ln \left (\frac {\ln \left (x-2\right )+x^2\,\ln \left (x^2\right )}{x\,\ln \left (x^2\right )}\right )\,\left (\left (2\,x^4-x^5\right )\,{\ln \left (x^2\right )}^2+\ln \left (x-2\right )\,\left (2\,x^2-x^3\right )\,\ln \left (x^2\right )\right )} \,d x \]
int(-(log(x/log((log(x - 2) + x^2*log(x^2))/(x*log(x^2))))*log((log(x - 2) + x^2*log(x^2))/(x*log(x^2)))*(log(x^2)^2*exp(x)*(2*x^2 - 3*x^3 + x^4) + log(x - 2)*log(x^2)*exp(x)*(x^2 - 3*x + 2)) - log((log(x - 2) + x^2*log(x^ 2))/(x*log(x^2)))*(log(x^2)^2*exp(x)*(2*x^2 - x^3) - log(x - 2)*log(x^2)*e xp(x)*(x - 2)) - log(x^2)*(x*exp(x) - log(x - 2)*exp(x)*(x - 2)) + log(x^2 )^2*exp(x)*(2*x^2 - x^3) + log(x - 2)*exp(x)*(2*x - 4))/(log((log(x - 2) + x^2*log(x^2))/(x*log(x^2)))*(log(x^2)^2*(2*x^4 - x^5) + log(x - 2)*log(x^ 2)*(2*x^2 - x^3))),x)
int(-(log(x/log((log(x - 2) + x^2*log(x^2))/(x*log(x^2))))*log((log(x - 2) + x^2*log(x^2))/(x*log(x^2)))*(log(x^2)^2*exp(x)*(2*x^2 - 3*x^3 + x^4) + log(x - 2)*log(x^2)*exp(x)*(x^2 - 3*x + 2)) - log((log(x - 2) + x^2*log(x^ 2))/(x*log(x^2)))*(log(x^2)^2*exp(x)*(2*x^2 - x^3) - log(x - 2)*log(x^2)*e xp(x)*(x - 2)) - log(x^2)*(x*exp(x) - log(x - 2)*exp(x)*(x - 2)) + log(x^2 )^2*exp(x)*(2*x^2 - x^3) + log(x - 2)*exp(x)*(2*x - 4))/(log((log(x - 2) + x^2*log(x^2))/(x*log(x^2)))*(log(x^2)^2*(2*x^4 - x^5) + log(x - 2)*log(x^ 2)*(2*x^2 - x^3))), x)