\[ \int \frac {e (1-x) \log (x)+\left (-x+x^2\right ) \log ^2(x)+\left (-2 e x+2 x^2 \log (x)\right ) \log (-3+3 x)+\left (e (1-x)+\left (-x+x^2\right ) \log (x)\right ) \log ^2(-3+3 x)+\left (e (-1+x)-x+x^2+\left (e (1-x)+x-x^2\right ) \log (x)+\left (e (1-x)+x-x^2\right ) \log ^2(-3+3 x)\right ) \log \left (-x+x \log (x)+x \log ^2(-3+3 x)\right )}{\left (x^2-x^3+\left (-x^2+x^3\right ) \log (x)+\left (-x^2+x^3\right ) \log ^2(-3+3 x)\right ) \log ^2\left (-x+x \log (x)+x \log ^2(-3+3 x)\right )} \, dx \]
Optimal antiderivative \[ \frac {\frac {{\mathrm e}}{x}-\ln \! \left (x \right )}{\ln \! \left (\left (\ln \! \left (x \right )+\ln \! \left (-3+3 x \right )^{2}\right ) x -x \right )} \]
command
int(((((1-x)*exp(1)-x^2+x)*ln(3*x-3)^2+((1-x)*exp(1)-x^2+x)*ln(x)+(x-1)*exp(1)+x^2-x)*ln(x*ln(3*x-3)^2+x*ln(x)-x)+(ln(x)*(x^2-x)+(1-x)*exp(1))*ln(3*x-3)^2+(2*x^2*ln(x)-2*x*exp(1))*ln(3*x-3)+(x^2-x)*ln(x)^2+(1-x)*exp(1)*ln(x))/((x^3-x^2)*ln(3*x-3)^2+(x^3-x^2)*ln(x)-x^3+x^2)/ln(x*ln(3*x-3)^2+x*ln(x)-x)^2,x)
Maple 2022.1 output
\[\int \frac {\left (\left (\left (1-x \right ) {\mathrm e}-x^{2}+x \right ) \ln \left (3 x -3\right )^{2}+\left (\left (1-x \right ) {\mathrm e}-x^{2}+x \right ) \ln \left (x \right )+\left (x -1\right ) {\mathrm e}+x^{2}-x \right ) \ln \left (x \ln \left (3 x -3\right )^{2}+x \ln \left (x \right )-x \right )+\left (\ln \left (x \right ) \left (x^{2}-x \right )+\left (1-x \right ) {\mathrm e}\right ) \ln \left (3 x -3\right )^{2}+\left (2 x^{2} \ln \left (x \right )-2 x \,{\mathrm e}\right ) \ln \left (3 x -3\right )+\left (x^{2}-x \right ) \ln \left (x \right )^{2}+\left (1-x \right ) {\mathrm e} \ln \left (x \right )}{\left (\left (x^{3}-x^{2}\right ) \ln \left (3 x -3\right )^{2}+\left (x^{3}-x^{2}\right ) \ln \left (x \right )-x^{3}+x^{2}\right ) \ln \left (x \ln \left (3 x -3\right )^{2}+x \ln \left (x \right )-x \right )^{2}}\, dx\]
Maple 2021.1 output
| method | result | size |
| risch | \(\frac {-2 x \ln \left (x \right )+2 \,{\mathrm e}}{x \left (2 \ln \left (x \right )+2 \ln \left (\ln \left (3 x -3\right )^{2}+\ln \left (x \right )-1\right )-i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (\ln \left (3 x -3\right )^{2}+\ln \left (x \right )-1\right )\right ) \mathrm {csgn}\left (i x \left (\ln \left (3 x -3\right )^{2}+\ln \left (x \right )-1\right )\right )+i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (\ln \left (3 x -3\right )^{2}+\ln \left (x \right )-1\right )\right )^{2}+i \pi \,\mathrm {csgn}\left (i \left (\ln \left (3 x -3\right )^{2}+\ln \left (x \right )-1\right )\right ) \mathrm {csgn}\left (i x \left (\ln \left (3 x -3\right )^{2}+\ln \left (x \right )-1\right )\right )^{2}-i \pi \mathrm {csgn}\left (i x \left (\ln \left (3 x -3\right )^{2}+\ln \left (x \right )-1\right )\right )^{3}\right )}\) | \(168\) |