33.3 Problem number 29

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

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

command

integrate(csch(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

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