\[ \int \frac {x^6}{\sqrt {a x^2+b x^5}} \, dx \]
Optimal antiderivative \[ -\frac {4 a \sqrt {b \,x^{5}+a \,x^{2}}}{9 b^{2} x}+\frac {2 x^{2} \sqrt {b \,x^{5}+a \,x^{2}}}{9 b} \]
command
integrate(x^6/(b*x^5+a*x^2)^(1/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {4 \, a^{\frac {3}{2}} \mathrm {sgn}\left (x\right )}{9 \, b^{2}} + \frac {2 \, {\left (b x^{3} + a\right )}^{\frac {3}{2}}}{9 \, b^{2} \mathrm {sgn}\left (x\right )} - \frac {2 \, \sqrt {b x^{3} + a} a}{3 \, b^{2} \mathrm {sgn}\left (x\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {x^{6}}{\sqrt {b x^{5} + a x^{2}}}\,{d x} \]________________________________________________________________________________________