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