\[ \int \frac {-30 x^2+e^{\frac {25+10 x+x^2}{x}} \left (-125+5 x^2\right )+6 x^2 \log (2)}{-75 x^2+5 e^{\frac {25+10 x+x^2}{x}} x^2-30 x^3+\left (15 x^2+6 x^3\right ) \log (2)} \, dx \]
Optimal antiderivative \[ \ln \! \left (2\right )+\ln \! \left (6 x +15+\frac {5 \,{\mathrm e}^{\frac {\left (5+x \right )^{2}}{x}}}{\ln \! \left (2\right )-5}\right ) \]
command
Int[(-30*x^2 + E^((25 + 10*x + x^2)/x)*(-125 + 5*x^2) + 6*x^2*Log[2])/(-75*x^2 + 5*E^((25 + 10*x + x^2)/x)*x^2 - 30*x^3 + (15*x^2 + 6*x^3)*Log[2]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {-30 x^2+e^{\frac {25+10 x+x^2}{x}} \left (-125+5 x^2\right )+6 x^2 \log (2)}{-75 x^2+5 e^{\frac {25+10 x+x^2}{x}} x^2-30 x^3+\left (15 x^2+6 x^3\right ) \log (2)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \log \left (5 e^{\frac {(x+5)^2}{x}}-(x (30-\log (64)))-15 (5-\log (2))\right ) \]