\[ \int \left (a+b \sqrt {x}\right )^p x \, dx \]
Optimal antiderivative \[ -\frac {2 a^{3} \left (a +b \sqrt {x}\right )^{1+p}}{b^{4} \left (1+p \right )}+\frac {6 a^{2} \left (a +b \sqrt {x}\right )^{2+p}}{b^{4} \left (2+p \right )}-\frac {6 a \left (a +b \sqrt {x}\right )^{3+p}}{b^{4} \left (3+p \right )}+\frac {2 \left (a +b \sqrt {x}\right )^{4+p}}{b^{4} \left (4+p \right )} \]
command
integrate(x*(a+b*x**(1/2))**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 \[ \text {Timed out} \]_____________________________________________________