17.1 Problem number 394

$$\int e^{2{\tanh }^{-1}(ax)}{x}^2\sqrt{c-acx}dx$$

Optimal antiderivative $$\frac{10{(-acx+c)}^{\frac{3}{2}}}{3a^{3}c}-\frac{8{(-acx+c)}^{\frac{5}{2}}}{5a^3{c}^2}+\frac{2{(-acx+c)}^{\frac{7}{2}}}{7a^3{c}^3}-\frac{4\sqrt{-acx+c}}{a^3}$$

command

int((a*x+1)^2/(-a^2*x^2+1)*x^2*(-a*c*x+c)^(1/2),x)

Maple 2022.1 output

hanged

Maple 2021.1 output

$$-\frac{2\sqrt{-acx+c}(15x^3{a}^3+39a^2{x}^2+52ax+104)}{105a^3}$$