\[ \int \frac {x^{4/3}}{(a+b x)^2} \, dx \]
Optimal antiderivative \[ \frac {4 x^{\frac {1}{3}}}{b^{2}}-\frac {x^{\frac {4}{3}}}{b \left (b x +a \right )}-\frac {2 a^{\frac {1}{3}} \ln \left (a^{\frac {1}{3}}+b^{\frac {1}{3}} x^{\frac {1}{3}}\right )}{b^{\frac {7}{3}}}+\frac {2 a^{\frac {1}{3}} \ln \left (b x +a \right )}{3 b^{\frac {7}{3}}}+\frac {4 a^{\frac {1}{3}} \arctan \left (\frac {\left (a^{\frac {1}{3}}-2 b^{\frac {1}{3}} x^{\frac {1}{3}}\right ) \sqrt {3}}{3 a^{\frac {1}{3}}}\right ) \sqrt {3}}{3 b^{\frac {7}{3}}} \]
command
integrate(x**(4/3)/(b*x+a)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} \tilde {\infty } \sqrt [3]{x} & \text {for}\: a = 0 \wedge b = 0 \\\frac {3 x^{\frac {7}{3}}}{7 a^{2}} & \text {for}\: b = 0 \\\frac {3 \sqrt [3]{x}}{b^{2}} & \text {for}\: a = 0 \\\frac {12 a \sqrt [3]{x}}{3 a b^{2} + 3 b^{3} x} + \frac {4 a \sqrt [3]{- \frac {a}{b}} \log {\left (\sqrt [3]{x} - \sqrt [3]{- \frac {a}{b}} \right )}}{3 a b^{2} + 3 b^{3} x} - \frac {2 a \sqrt [3]{- \frac {a}{b}} \log {\left (4 x^{\frac {2}{3}} + 4 \sqrt [3]{x} \sqrt [3]{- \frac {a}{b}} + 4 \left (- \frac {a}{b}\right )^{\frac {2}{3}} \right )}}{3 a b^{2} + 3 b^{3} x} - \frac {4 \sqrt {3} a \sqrt [3]{- \frac {a}{b}} \operatorname {atan}{\left (\frac {2 \sqrt {3} \sqrt [3]{x}}{3 \sqrt [3]{- \frac {a}{b}}} + \frac {\sqrt {3}}{3} \right )}}{3 a b^{2} + 3 b^{3} x} + \frac {4 a \sqrt [3]{- \frac {a}{b}} \log {\left (2 \right )}}{3 a b^{2} + 3 b^{3} x} + \frac {9 b x^{\frac {4}{3}}}{3 a b^{2} + 3 b^{3} x} + \frac {4 b x \sqrt [3]{- \frac {a}{b}} \log {\left (\sqrt [3]{x} - \sqrt [3]{- \frac {a}{b}} \right )}}{3 a b^{2} + 3 b^{3} x} - \frac {2 b x \sqrt [3]{- \frac {a}{b}} \log {\left (4 x^{\frac {2}{3}} + 4 \sqrt [3]{x} \sqrt [3]{- \frac {a}{b}} + 4 \left (- \frac {a}{b}\right )^{\frac {2}{3}} \right )}}{3 a b^{2} + 3 b^{3} x} - \frac {4 \sqrt {3} b x \sqrt [3]{- \frac {a}{b}} \operatorname {atan}{\left (\frac {2 \sqrt {3} \sqrt [3]{x}}{3 \sqrt [3]{- \frac {a}{b}}} + \frac {\sqrt {3}}{3} \right )}}{3 a b^{2} + 3 b^{3} x} + \frac {4 b x \sqrt [3]{- \frac {a}{b}} \log {\left (2 \right )}}{3 a b^{2} + 3 b^{3} x} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________