\[ \int \frac {\left (7 x-7 x^3\right ) \log (x)+\left (28 x-28 x^2\right ) \log ^2(x)+\left (2-2 x^2+4 x^2 \log (x)+8 x \log ^2(x)\right ) \log \left (\frac {1-x^2+(4-4 x) \log (x)}{4 \log (x)}\right )}{\left (-x+x^3\right ) \log (x)+\left (-4 x+4 x^2\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \ln \left (1-x -\frac {x^{2}-1}{4 \ln \left (x \right )}\right )^{2}-7 x \]
command
int(((8*x*ln(x)^2+4*x^2*ln(x)-2*x^2+2)*ln(1/4*((-4*x+4)*ln(x)-x^2+1)/ln(x))+(-28*x^2+28*x)*ln(x)^2+(-7*x^3+7*x)*ln(x))/((4*x^2-4*x)*ln(x)^2+(x^3-x)*ln(x)),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(-7 x -4 \ln \left (2\right ) \ln \left (x -1\right )-4 \ln \left (2\right ) \ln \left (x +4 \ln \left (x \right )+1\right )+4 \ln \left (2\right ) \ln \left (\ln \left (x \right )\right )+\ln \left (-\frac {4 x \ln \left (x \right )+x^{2}-4 \ln \left (x \right )-1}{\ln \left (x \right )}\right )^{2}\) | \(55\) |
Maple 2021.1 output
\[\int \frac {\left (8 x \ln \left (x \right )^{2}+4 x^{2} \ln \left (x \right )-2 x^{2}+2\right ) \ln \left (\frac {\left (-4 x +4\right ) \ln \left (x \right )-x^{2}+1}{4 \ln \left (x \right )}\right )+\left (-28 x^{2}+28 x \right ) \ln \left (x \right )^{2}+\left (-7 x^{3}+7 x \right ) \ln \left (x \right )}{\left (4 x^{2}-4 x \right ) \ln \left (x \right )^{2}+\left (x^{3}-x \right ) \ln \left (x \right )}\, dx\]________________________________________________________________________________________