\[ \int \frac {\coth (c+d x)}{a+b \text {sech}^2(c+d x)} \, dx \]
Optimal antiderivative \[ \frac {b \ln \! \left (b +a \left (\cosh ^{2}\left (d x +c \right )\right )\right )}{2 a \left (a +b \right ) d}+\frac {\ln \! \left (\sinh \! \left (d x +c \right )\right )}{\left (a +b \right ) d} \]
command
integrate(coth(d*x+c)/(a+b*sech(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
\[ -\frac {\frac {2 \, d x}{a} - \frac {b \log \left (a e^{\left (4 \, d x + 4 \, c\right )} + 2 \, a e^{\left (2 \, d x + 2 \, c\right )} + 4 \, b e^{\left (2 \, d x + 2 \, c\right )} + a\right )}{a^{2} + a b} - \frac {2 \, e^{\left (2 \, c\right )} \log \left ({\left | e^{\left (2 \, d x + 2 \, c\right )} - 1 \right |}\right )}{a e^{\left (2 \, c\right )} + b e^{\left (2 \, c\right )}}}{2 \, d} \]