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