\[ \int \frac {x^2}{\left (b x^{2/3}+a x\right )^{3/2}} \, dx \]
Optimal antiderivative \[ -\frac {6 x^{2}}{a \sqrt {b \,x^{\frac {2}{3}}+a x}}-\frac {256 b^{3} \sqrt {b \,x^{\frac {2}{3}}+a x}}{21 a^{5}}+\frac {512 b^{4} \sqrt {b \,x^{\frac {2}{3}}+a x}}{21 a^{6} x^{\frac {1}{3}}}+\frac {64 b^{2} x^{\frac {1}{3}} \sqrt {b \,x^{\frac {2}{3}}+a x}}{7 a^{4}}-\frac {160 b \,x^{\frac {2}{3}} \sqrt {b \,x^{\frac {2}{3}}+a x}}{21 a^{3}}+\frac {20 x \sqrt {b \,x^{\frac {2}{3}}+a x}}{3 a^{2}} \]
command
integrate(x^2/(b*x^(2/3)+a*x)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ \text {Timed out} \]