\[ \int \frac {a-b x^3}{\left (a+b x^3\right )^{10/3}} \, dx \]
Optimal antiderivative \[ \frac {2 x}{7 \left (b \,x^{3}+a \right )^{\frac {7}{3}}}+\frac {5 x}{28 a \left (b \,x^{3}+a \right )^{\frac {4}{3}}}+\frac {15 x}{28 a^{2} \left (b \,x^{3}+a \right )^{\frac {1}{3}}} \]
command
integrate((-b*x**3+a)/(b*x**3+a)**(10/3),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ a \left (\frac {28 a^{5} x \Gamma \left (\frac {1}{3}\right )}{27 a^{\frac {25}{3}} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 81 a^{\frac {22}{3}} b x^{3} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 81 a^{\frac {19}{3}} b^{2} x^{6} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 27 a^{\frac {16}{3}} b^{3} x^{9} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right )} + \frac {70 a^{4} b x^{4} \Gamma \left (\frac {1}{3}\right )}{27 a^{\frac {25}{3}} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 81 a^{\frac {22}{3}} b x^{3} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 81 a^{\frac {19}{3}} b^{2} x^{6} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 27 a^{\frac {16}{3}} b^{3} x^{9} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right )} + \frac {60 a^{3} b^{2} x^{7} \Gamma \left (\frac {1}{3}\right )}{27 a^{\frac {25}{3}} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 81 a^{\frac {22}{3}} b x^{3} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 81 a^{\frac {19}{3}} b^{2} x^{6} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 27 a^{\frac {16}{3}} b^{3} x^{9} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right )} + \frac {18 a^{2} b^{3} x^{10} \Gamma \left (\frac {1}{3}\right )}{27 a^{\frac {25}{3}} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 81 a^{\frac {22}{3}} b x^{3} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 81 a^{\frac {19}{3}} b^{2} x^{6} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 27 a^{\frac {16}{3}} b^{3} x^{9} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right )}\right ) - b \left (\frac {7 a x^{4} \Gamma \left (\frac {4}{3}\right )}{9 a^{\frac {13}{3}} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 18 a^{\frac {10}{3}} b x^{3} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 9 a^{\frac {7}{3}} b^{2} x^{6} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right )} + \frac {3 b x^{7} \Gamma \left (\frac {4}{3}\right )}{9 a^{\frac {13}{3}} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 18 a^{\frac {10}{3}} b x^{3} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right ) + 9 a^{\frac {7}{3}} b^{2} x^{6} \sqrt [3]{1 + \frac {b x^{3}}{a}} \Gamma \left (\frac {10}{3}\right )}\right ) \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________