33.2 Problem number 28

\[ \int \frac {\sinh (c+d x)}{a+b \tanh ^2(c+d x)} \, dx \]

Optimal antiderivative \[ \frac {\cosh \! \left (d x +c \right )}{\left (a +b \right ) d}-\frac {\arctanh \! \left (\frac {\mathrm {sech}\left (d x +c \right ) \sqrt {b}}{\sqrt {a +b}}\right ) \sqrt {b}}{\left (a +b \right )^{\frac {3}{2}} d} \]

command

integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \text {Exception raised: TypeError} \]

Giac 1.7.0 via sagemath 9.3 output

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