\[ \int \frac {\left (-20+104 x-40 x^2+4 x^3+\left (100 x-40 x^2+4 x^3\right ) \log (4)-20 \log (x)\right ) \log \left (\frac {5-x+5 x^2-x^3+\left (5 x^2-x^3\right ) \log (4)-2 x \log (x)}{-25+5 x}\right )}{25-10 x+26 x^2-10 x^3+x^4+\left (25 x^2-10 x^3+x^4\right ) \log (4)+\left (-10 x+2 x^2\right ) \log (x)} \, dx \]
Optimal antiderivative \[ \ln \left (\frac {2 \ln \left (x \right ) x}{5 \left (5-x \right )}-\frac {2 x^{2} \ln \left (2\right )}{5}-\frac {x^{2}}{5}-\frac {1}{5}\right )^{2} \]
command
int((-20*ln(x)+2*(4*x^3-40*x^2+100*x)*ln(2)+4*x^3-40*x^2+104*x-20)*ln((-2*x*ln(x)+2*(-x^3+5*x^2)*ln(2)-x^3+5*x^2-x+5)/(5*x-25))/((2*x^2-10*x)*ln(x)+2*(x^4-10*x^3+25*x^2)*ln(2)+x^4-10*x^3+26*x^2-10*x+25),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(\text {Expression too large to display}\) | \(1051\) |
Maple 2021.1 output
\[\int \frac {\left (-20 \ln \left (x \right )+2 \left (4 x^{3}-40 x^{2}+100 x \right ) \ln \left (2\right )+4 x^{3}-40 x^{2}+104 x -20\right ) \ln \left (\frac {-2 x \ln \left (x \right )+2 \left (-x^{3}+5 x^{2}\right ) \ln \left (2\right )-x^{3}+5 x^{2}-x +5}{5 x -25}\right )}{\left (2 x^{2}-10 x \right ) \ln \left (x \right )+2 \left (x^{4}-10 x^{3}+25 x^{2}\right ) \ln \left (2\right )+x^{4}-10 x^{3}+26 x^{2}-10 x +25}\, dx\]________________________________________________________________________________________