\[ \int \frac {-2+3 x^5}{\sqrt {1+x^5} \left (a-x^2+a x^5\right )} \, dx \]
Optimal antiderivative \[ -\frac {2 \arctanh \left (\frac {x}{\sqrt {a}\, \sqrt {x^{5}+1}}\right )}{\sqrt {a}} \]
command
Integrate[(-2 + 3*x^5)/(Sqrt[1 + x^5]*(a - x^2 + a*x^5)),x]
Mathematica 13.1 output
\[ -\frac {2 \tanh ^{-1}\left (\frac {x}{\sqrt {a} \sqrt {1+x^5}}\right )}{\sqrt {a}} \]
Mathematica 12.3 output
\[ \int \frac {-2+3 x^5}{\sqrt {1+x^5} \left (a-x^2+a x^5\right )} \, dx \]________________________________________________________________________________________