\[ \int \frac {200 x^2+80 x^3+\left (-50 x^3-20 x^4\right ) \log (x)+\left (-400 x-160 x^2+\left (100 x^2+40 x^3\right ) \log (x)\right ) \log \left (x^2\right )+\left (200+80 x+\left (-50 x-20 x^2\right ) \log (x)\right ) \log ^2\left (x^2\right )+\left (\frac {4-x \log (x)}{x}\right )^{\frac {x}{-2 x+2 \log \left (x^2\right )}} \left (-100 x-85 x^2-5 x^3+10 x^3 \log (x)+\left (100+125 x+5 x^2-20 x^2 \log (x)\right ) \log \left (x^2\right )+(-40+10 x \log (x)) \log ^2\left (x^2\right )+\left (200+40 x+\left (-50 x-10 x^2\right ) \log (x)+\left (-100-20 x+\left (25 x+5 x^2\right ) \log (x)\right ) \log \left (x^2\right )\right ) \log \left (\frac {4-x \log (x)}{x}\right )\right )}{-8 x^2+2 x^3 \log (x)+\left (16 x-4 x^2 \log (x)\right ) \log \left (x^2\right )+(-8+2 x \log (x)) \log ^2\left (x^2\right )} \, dx \]
Optimal antiderivative \[ \left ({\mathrm e}^{\frac {x \ln \left (\frac {4}{x}-\ln \left (x \right )\right )}{2 \ln \left (x^{2}\right )-2 x}}-x \right ) \left (25+5 x \right ) \]
command
int((((((5*x^2+25*x)*ln(x)-20*x-100)*ln(x^2)+(-10*x^2-50*x)*ln(x)+40*x+200)*ln((-x*ln(x)+4)/x)+(10*x*ln(x)-40)*ln(x^2)^2+(-20*x^2*ln(x)+5*x^2+125*x+100)*ln(x^2)+10*x^3*ln(x)-5*x^3-85*x^2-100*x)*exp(x*ln((-x*ln(x)+4)/x)/(2*ln(x^2)-2*x))+((-20*x^2-50*x)*ln(x)+80*x+200)*ln(x^2)^2+((40*x^3+100*x^2)*ln(x)-160*x^2-400*x)*ln(x^2)+(-20*x^4-50*x^3)*ln(x)+80*x^3+200*x^2)/((2*x*ln(x)-8)*ln(x^2)^2+(-4*x^2*ln(x)+16*x)*ln(x^2)+2*x^3*ln(x)-8*x^2),x)
Maple 2022.1 output
\[\int \frac {\left (\left (\left (\left (5 x^{2}+25 x \right ) \ln \left (x \right )-20 x -100\right ) \ln \left (x^{2}\right )+\left (-10 x^{2}-50 x \right ) \ln \left (x \right )+40 x +200\right ) \ln \left (\frac {-x \ln \left (x \right )+4}{x}\right )+\left (10 x \ln \left (x \right )-40\right ) \ln \left (x^{2}\right )^{2}+\left (-20 x^{2} \ln \left (x \right )+5 x^{2}+125 x +100\right ) \ln \left (x^{2}\right )+10 x^{3} \ln \left (x \right )-5 x^{3}-85 x^{2}-100 x \right ) {\mathrm e}^{\frac {x \ln \left (\frac {-x \ln \left (x \right )+4}{x}\right )}{2 \ln \left (x^{2}\right )-2 x}}+\left (\left (-20 x^{2}-50 x \right ) \ln \left (x \right )+80 x +200\right ) \ln \left (x^{2}\right )^{2}+\left (\left (40 x^{3}+100 x^{2}\right ) \ln \left (x \right )-160 x^{2}-400 x \right ) \ln \left (x^{2}\right )+\left (-20 x^{4}-50 x^{3}\right ) \ln \left (x \right )+80 x^{3}+200 x^{2}}{\left (2 x \ln \left (x \right )-8\right ) \ln \left (x^{2}\right )^{2}+\left (-4 x^{2} \ln \left (x \right )+16 x \right ) \ln \left (x^{2}\right )+2 x^{3} \ln \left (x \right )-8 x^{2}}\, dx\]
Maple 2021.1 output
| method | result | size |
| risch | \(-5 x^{2}-25 x +\left (25+5 x \right ) {\mathrm e}^{-\frac {x \left (-i \pi \mathrm {csgn}\left (\frac {i \left (x \ln \left (x \right )-4\right )}{x}\right )^{3}-i \pi \mathrm {csgn}\left (\frac {i \left (x \ln \left (x \right )-4\right )}{x}\right )^{2} \mathrm {csgn}\left (\frac {i}{x}\right )-i \pi \mathrm {csgn}\left (\frac {i \left (x \ln \left (x \right )-4\right )}{x}\right )^{2} \mathrm {csgn}\left (i \left (x \ln \left (x \right )-4\right )\right )+i \pi \,\mathrm {csgn}\left (\frac {i \left (x \ln \left (x \right )-4\right )}{x}\right ) \mathrm {csgn}\left (\frac {i}{x}\right ) \mathrm {csgn}\left (i \left (x \ln \left (x \right )-4\right )\right )+2 i \pi \mathrm {csgn}\left (\frac {i \left (x \ln \left (x \right )-4\right )}{x}\right )^{2}-2 i \pi +2 \ln \left (x \right )-2 \ln \left (x \ln \left (x \right )-4\right )\right )}{2 \left (-i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}+2 i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-i \pi \mathrm {csgn}\left (i x \right )^{2} \mathrm {csgn}\left (i x^{2}\right )+4 \ln \left (x \right )-2 x \right )}}\) | \(224\) |