\[ \int e^{2 \tanh ^{-1}(a x)} x^2 \sqrt {c-a c x} \, dx \]
Optimal antiderivative \[ \frac {10 \left (-a c x +c \right )^{\frac {3}{2}}}{3 a^{3} c}-\frac {8 \left (-a c x +c \right )^{\frac {5}{2}}}{5 a^{3} c^{2}}+\frac {2 \left (-a c x +c \right )^{\frac {7}{2}}}{7 a^{3} c^{3}}-\frac {4 \sqrt {-a c x +c}}{a^{3}} \]
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
\[ -\frac {2 \sqrt {-a c x +c}\, \left (15 x^{3} a^{3}+39 a^{2} x^{2}+52 a x +104\right )}{105 a^{3}} \]