\[ \int \frac {x^2 \sqrt {q+p x^5} \left (-2 q+3 p x^5\right )}{b x^6+a \left (q+p x^5\right )^3} \, dx \]
Optimal antiderivative \[ -\frac {2 \arctan \left (\frac {\sqrt {b}\, x^{3}}{\sqrt {a}\, \left (p \,x^{5}+q \right )^{\frac {3}{2}}}\right )}{3 \sqrt {a}\, \sqrt {b}} \]
command
Integrate[(x^2*Sqrt[q + p*x^5]*(-2*q + 3*p*x^5))/(b*x^6 + a*(q + p*x^5)^3),x]
Mathematica 13.1 output
\[ -\frac {2 \text {ArcTan}\left (\frac {\sqrt {b} x^3}{\sqrt {a} \left (q+p x^5\right )^{3/2}}\right )}{3 \sqrt {a} \sqrt {b}} \]
Mathematica 12.3 output
\[ \int \frac {x^2 \sqrt {q+p x^5} \left (-2 q+3 p x^5\right )}{b x^6+a \left (q+p x^5\right )^3} \, dx \]________________________________________________________________________________________