\[ \int \frac {1}{\frac {1}{\sqrt [3]{x}}+\frac {1}{\sqrt [4]{x}}} \, dx \]
Optimal antiderivative \[ 12 x^{\frac {1}{12}}-6 x^{\frac {1}{6}}+4 x^{\frac {1}{4}}-3 x^{\frac {1}{3}}+\frac {12 x^{\frac {5}{12}}}{5}+\frac {12 x^{\frac {7}{12}}}{7}-\frac {3 x^{\frac {2}{3}}}{2}+\frac {4 x^{\frac {3}{4}}}{3}-\frac {6 x^{\frac {5}{6}}}{5}+\frac {12 x^{\frac {11}{12}}}{11}-x +\frac {12 x^{\frac {13}{12}}}{13}-\frac {6 x^{\frac {7}{6}}}{7}+\frac {4 x^{\frac {5}{4}}}{5}-12 \ln \! \left (1+x^{\frac {1}{12}}\right )-2 \sqrt {x} \]
command
integrate(1/(1/x**(1/3)+1/x**(1/4)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \int \frac {x^{\frac {7}{12}}}{\sqrt [4]{x} + \sqrt [3]{x}}\, dx \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {12 x^{\frac {13}{12}}}{13} + \frac {12 x^{\frac {11}{12}}}{11} + \frac {12 x^{\frac {7}{12}}}{7} + \frac {12 x^{\frac {5}{12}}}{5} + 12 \sqrt [12]{x} - \frac {6 x^{\frac {7}{6}}}{7} - \frac {6 x^{\frac {5}{6}}}{5} - 6 \sqrt [6]{x} + \frac {4 x^{\frac {5}{4}}}{5} + \frac {4 x^{\frac {3}{4}}}{3} + 4 \sqrt [4]{x} - \frac {3 x^{\frac {2}{3}}}{2} - 3 \sqrt [3]{x} - 2 \sqrt {x} - x - 12 \log {\left (\sqrt [12]{x} + 1 \right )} \]