\[ \int \frac {-4+x}{\left (1+\sqrt [3]{x}\right ) \sqrt {x}} \, dx \]
Optimal antiderivative \[ -30 x^{\frac {1}{6}}-\frac {6 x^{\frac {5}{6}}}{5}+\frac {6 x^{\frac {7}{6}}}{7}+30 \arctan \! \left (x^{\frac {1}{6}}\right )+2 \sqrt {x} \]
command
integrate((-4+x)/(1+x**(1/3))/x**(1/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \int \frac {x - 4}{\sqrt {x} \left (\sqrt [3]{x} + 1\right )}\, dx \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {6 x^{\frac {7}{6}}}{7} - \frac {6 x^{\frac {5}{6}}}{5} - 30 \sqrt [6]{x} + 2 \sqrt {x} + 30 \operatorname {atan}{\left (\sqrt [6]{x} \right )} \]