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