18.2 Problem number 148

\[ \int x^3 \coth ^{-1}(\tanh (a+b x))^3 \, dx \]

Optimal antiderivative \[ -\frac {b^{3} x^{7}}{140}+\frac {b^{2} x^{6} \mathrm {arccoth}\! \left (\tanh \! \left (b x +a \right )\right )}{20}-\frac {3 b \,x^{5} \mathrm {arccoth}\! \left (\tanh \! \left (b x +a \right )\right )^{2}}{20}+\frac {x^{4} \mathrm {arccoth}\! \left (\tanh \! \left (b x +a \right )\right )^{3}}{4} \]

command

int(x^3*arccoth(tanh(b*x+a))^3,x)

Maple 2022.1 output

\[\int x^{3} \mathrm {arccoth}\left (\tanh \left (b x +a \right )\right )^{3}\, dx\]

Maple 2021.1 output

\[ \text {output too large to display} \]