\[ \int \frac {\left (216+324 x+72 x^2-80 x^3-32 x^4\right ) \log ^3\left (\frac {-24-25 x-6 x^2}{4+4 x+x^2}\right )+\left (3456+9936 x+11304 x^2+6352 x^3+1760 x^4+192 x^5\right ) \log ^4\left (\frac {-24-25 x-6 x^2}{4+4 x+x^2}\right )}{16+14 x+3 x^2} \, dx \]
Optimal antiderivative \[ \ln \left (-6-\frac {x}{\left (2+x \right )^{2}}\right )^{4} \left (3+2 x \right )^{4} \]
command
int(((192*x^5+1760*x^4+6352*x^3+11304*x^2+9936*x+3456)*ln((-6*x^2-25*x-24)/(x^2+4*x+4))^4+(-32*x^4-80*x^3+72*x^2+324*x+216)*ln((-6*x^2-25*x-24)/(x^2+4*x+4))^3)/(3*x^2+14*x+16),x,method=_RETURNVERBOSE)
Maple 2022.1 output
| method | result | size |
| risch | \(\left (2 x +3\right )^{4} \ln \left (\frac {-6 x^{2}-25 x -24}{x^{2}+4 x +4}\right )^{4}\) | \(33\) |
Maple 2021.1 output
\[\int \frac {\left (192 x^{5}+1760 x^{4}+6352 x^{3}+11304 x^{2}+9936 x +3456\right ) \ln \left (\frac {-6 x^{2}-25 x -24}{x^{2}+4 x +4}\right )^{4}+\left (-32 x^{4}-80 x^{3}+72 x^{2}+324 x +216\right ) \ln \left (\frac {-6 x^{2}-25 x -24}{x^{2}+4 x +4}\right )^{3}}{3 x^{2}+14 x +16}\, dx\]________________________________________________________________________________________