\[ \int \frac {a+b \text {ArcTan}\left (c x^3\right )}{x^{10}} \, dx \]
Optimal antiderivative \[ -\frac {b c}{18 x^{6}}+\frac {-a -b \arctan \left (c \,x^{3}\right )}{9 x^{9}}-\frac {b \,c^{3} \ln \left (x \right )}{3}+\frac {b \,c^{3} \ln \left (c^{2} x^{6}+1\right )}{18} \]
command
integrate((a+b*atan(c*x**3))/x**10,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \begin {cases} - \frac {a}{9 x^{9}} - \frac {b c^{4} \sqrt {- \frac {1}{c^{2}}} \operatorname {atan}{\left (c x^{3} \right )}}{9} - \frac {b c^{3} \log {\left (x \right )}}{3} + \frac {b c^{3} \log {\left (x - \sqrt [6]{- \frac {1}{c^{2}}} \right )}}{9} + \frac {b c^{3} \log {\left (4 x^{2} + 4 x \sqrt [6]{- \frac {1}{c^{2}}} + 4 \sqrt [3]{- \frac {1}{c^{2}}} \right )}}{9} - \frac {b c}{18 x^{6}} - \frac {b \operatorname {atan}{\left (c x^{3} \right )}}{9 x^{9}} & \text {for}\: c \neq 0 \\- \frac {a}{9 x^{9}} & \text {otherwise} \end {cases} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________