\[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{{\mathrm e}^{x}-\ln \left (\left (x +\ln \left (1+\ln \left (\left (2-x \right )^{2}\right )\right )\right )^{2}+5-2 x \right )} x \]
command
int(((((x^2-2*x)*exp(x)+x-2)*ln(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*ln(ln(x^2-4*x+4)+1)^2+((2*x^3-4*x^2)*exp(x)*ln(x^2-4*x+4)+(2*x^3-4*x^2)*exp(x)-4*x)*ln(ln(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^2+5*x-10)*ln(x^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp(-ln(ln(ln(x^2-4*x+4)+1)^2+2*x*ln(ln(x^2-4*x+4)+1)+x^2-2*x+5)+exp(x))/(((x-2)*ln(x^2-4*x+4)+x-2)*ln(ln(x^2-4*x+4)+1)^2+((2*x^2-4*x)*ln(x^2-4*x+4)+2*x^2-4*x)*ln(ln(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*ln(x^2-4*x+4)+x^3-4*x^2+9*x-10),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\frac {x \,{\mathrm e}^{{\mathrm e}^{x}}}{\ln \left (2 \ln \left (x -2\right )-\frac {i \pi \,\mathrm {csgn}\left (i \left (x -2\right )^{2}\right ) \left (-\mathrm {csgn}\left (i \left (x -2\right )^{2}\right )+\mathrm {csgn}\left (i \left (x -2\right )\right )\right )^{2}}{2}+1\right )^{2}+2 x \ln \left (2 \ln \left (x -2\right )-\frac {i \pi \,\mathrm {csgn}\left (i \left (x -2\right )^{2}\right ) \left (-\mathrm {csgn}\left (i \left (x -2\right )^{2}\right )+\mathrm {csgn}\left (i \left (x -2\right )\right )\right )^{2}}{2}+1\right )+x^{2}-2 x +5}\) | \(107\) |
Maple 2021.1 output
\[\int \frac {\left (\left (\left (\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )^{2}+\left (\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x} \ln \left (x^{2}-4 x +4\right )+\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}+2 x^{2}+5 x -10\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}-2 x^{2}+5 x -10\right ) {\mathrm e}^{-\ln \left (\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )^{2}+2 x \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+x^{2}-2 x +5\right )+{\mathrm e}^{x}}}{\left (\left (x -2\right ) \ln \left (x^{2}-4 x +4\right )+x -2\right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )^{2}+\left (\left (2 x^{2}-4 x \right ) \ln \left (x^{2}-4 x +4\right )+2 x^{2}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (x^{3}-4 x^{2}+9 x -10\right ) \ln \left (x^{2}-4 x +4\right )+x^{3}-4 x^{2}+9 x -10}\, dx\]________________________________________________________________________________________