\[ \int \frac {1}{\sqrt [3]{x} (a+b x)^3} \, dx \]
Optimal antiderivative \[ \frac {x^{\frac {2}{3}}}{2 a \left (b x +a \right )^{2}}+\frac {2 x^{\frac {2}{3}}}{3 a^{2} \left (b x +a \right )}-\frac {\ln \left (a^{\frac {1}{3}}+b^{\frac {1}{3}} x^{\frac {1}{3}}\right )}{3 a^{\frac {7}{3}} b^{\frac {2}{3}}}+\frac {\ln \left (b x +a \right )}{9 a^{\frac {7}{3}} b^{\frac {2}{3}}}-\frac {2 \arctan \left (\frac {\left (a^{\frac {1}{3}}-2 b^{\frac {1}{3}} x^{\frac {1}{3}}\right ) \sqrt {3}}{3 a^{\frac {1}{3}}}\right ) \sqrt {3}}{9 a^{\frac {7}{3}} b^{\frac {2}{3}}} \]
command
integrate(1/x**(1/3)/(b*x+a)**3,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________