\[ \int \frac {2400+1176 x+102 x^2-6 x^3+\left (800+392 x+34 x^2-2 x^3\right ) \log \left (\frac {x+x^2+(-100-25 x) \log (x)}{100+25 x}\right )}{-4 x^2-5 x^3-x^4+\left (400 x+200 x^2+25 x^3\right ) \log (x)} \, dx \]
Optimal antiderivative \[ \left (3+\ln \left (\frac {x^{2}+x}{25 x +100}-\ln \left (x \right )\right )\right )^{2} \]
command
int(((-2*x^3+34*x^2+392*x+800)*ln(((-25*x-100)*ln(x)+x^2+x)/(25*x+100))-6*x^3+102*x^2+1176*x+2400)/((25*x^3+200*x^2+400*x)*ln(x)-x^4-5*x^3-4*x^2),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| default | \(6 \ln \left (25 x \ln \left (x \right )-x^{2}+100 \ln \left (x \right )-x \right )-6 \ln \left (4+x \right )-4 \ln \left (5\right ) \ln \left (25 x \ln \left (x \right )-x^{2}+100 \ln \left (x \right )-x \right )+4 \ln \left (5\right ) \ln \left (4+x \right )+\ln \left (\frac {-25 x \ln \left (x \right )+x^{2}-100 \ln \left (x \right )+x}{4+x}\right )^{2}\) | \(83\) |
Maple 2021.1 output
\[\int \frac {\left (-2 x^{3}+34 x^{2}+392 x +800\right ) \ln \left (\frac {\left (-25 x -100\right ) \ln \left (x \right )+x^{2}+x}{25 x +100}\right )-6 x^{3}+102 x^{2}+1176 x +2400}{\left (25 x^{3}+200 x^{2}+400 x \right ) \ln \left (x \right )-x^{4}-5 x^{3}-4 x^{2}}\, dx\]________________________________________________________________________________________