7.2 Problem number 438

\[ \int \sqrt {x} (a+b x)^2 \, dx \]

Optimal antiderivative \[ \frac {2 a^{2} x^{\frac {3}{2}}}{3}+\frac {4 a b \,x^{\frac {5}{2}}}{5}+\frac {2 b^{2} x^{\frac {7}{2}}}{7} \]

command

integrate((b*x+a)**2*x**(1/2),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 \[ \text {Timed out} \]_____________________________________________________