\[ \int \frac {4-12 x-15 x^2-4 x^3+e^3 \left (-4-4 x-x^2\right )+\left (-20 x-18 x^2-4 x^3\right ) \log \left (\frac {2}{x}\right )+\left (-4 x-2 x^2-4 x \log \left (\frac {2}{x}\right )\right ) \log (x)}{4 x-28 x^2+33 x^3+56 x^4+16 x^5+e^6 \left (4 x+4 x^2+x^3\right )+e^3 \left (-8 x+24 x^2+30 x^3+8 x^4\right )+\left (-8 x^2+28 x^3+16 x^4+e^3 \left (8 x^2+4 x^3\right )\right ) \log (x)+4 x^3 \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {\ln \! \left (\frac {2}{x}\right )}{2 \left (\frac {\ln \left (x \right )}{2+x}+2\right ) x +{\mathrm e}^{3}-1} \]
command
int(((-4*x*ln(2/x)-2*x^2-4*x)*ln(x)+(-4*x^3-18*x^2-20*x)*ln(2/x)+(-x^2-4*x-4)*exp(3)-4*x^3-15*x^2-12*x+4)/(4*x^3*ln(x)^2+((4*x^3+8*x^2)*exp(3)+16*x^4+28*x^3-8*x^2)*ln(x)+(x^3+4*x^2+4*x)*exp(3)^2+(8*x^4+30*x^3+24*x^2-8*x)*exp(3)+16*x^5+56*x^4+33*x^3-28*x^2+4*x),x)
Maple 2022.1 output
\[\int \frac {\left (-4 x \ln \left (\frac {2}{x}\right )-2 x^{2}-4 x \right ) \ln \left (x \right )+\left (-4 x^{3}-18 x^{2}-20 x \right ) \ln \left (\frac {2}{x}\right )+\left (-x^{2}-4 x -4\right ) {\mathrm e}^{3}-4 x^{3}-15 x^{2}-12 x +4}{4 x^{3} \ln \left (x \right )^{2}+\left (\left (4 x^{3}+8 x^{2}\right ) {\mathrm e}^{3}+16 x^{4}+28 x^{3}-8 x^{2}\right ) \ln \left (x \right )+\left (x^{3}+4 x^{2}+4 x \right ) {\mathrm e}^{6}+\left (8 x^{4}+30 x^{3}+24 x^{2}-8 x \right ) {\mathrm e}^{3}+16 x^{5}+56 x^{4}+33 x^{3}-28 x^{2}+4 x}\, dx\]
Maple 2021.1 output
| method | result | size |
| risch | \(-\frac {1}{x}+\frac {-4+2 x^{2} \ln \left (2\right )+x^{2} {\mathrm e}^{3}+4 x^{3}+4 x \ln \left (2\right )+4 x \,{\mathrm e}^{3}+15 x^{2}+4 \,{\mathrm e}^{3}+12 x}{2 x \left (2 x \ln \left (x \right )+x \,{\mathrm e}^{3}+4 x^{2}+2 \,{\mathrm e}^{3}+7 x -2\right )}\) | \(79\) |