\[ \int (c x)^{-1-4 n-n p} \left (a+b x^n\right )^p \, dx \]
Optimal antiderivative \[ -\frac {\left (a +b \,x^{n}\right )^{1+p} \left (c x \right )^{-n \left (4+p \right )}}{a c n \left (1+p \right )}+\frac {3 \left (a +b \,x^{n}\right )^{2+p} \left (c x \right )^{-n \left (4+p \right )}}{a^{2} c n \left (1+p \right ) \left (2+p \right )}-\frac {6 \left (a +b \,x^{n}\right )^{3+p} \left (c x \right )^{-n \left (4+p \right )}}{a^{3} c n \left (1+p \right ) \left (2+p \right ) \left (3+p \right )}+\frac {6 \left (a +b \,x^{n}\right )^{4+p} \left (c x \right )^{-n \left (4+p \right )}}{a^{4} c n \left (p^{2}+3 p +2\right ) \left (p^{2}+7 p +12\right )} \]
command
integrate((c*x)**(-n*p-4*n-1)*(a+b*x**n)**p,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________