\[ \int \frac {\coth ^2(c+d x)}{a+b \text {sech}^2(c+d x)} \, dx \]
Optimal antiderivative \[ \frac {x}{a}-\frac {b^{\frac {3}{2}} \arctanh \left (\frac {\sqrt {b}\, \tanh \left (d x +c \right )}{\sqrt {a +b}}\right )}{a \left (a +b \right )^{\frac {3}{2}} d}-\frac {\coth \left (d x +c \right )}{\left (a +b \right ) d} \]
command
integrate(coth(d*x+c)^2/(a+b*sech(d*x+c)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {\frac {b^{2} \arctan \left (\frac {a e^{\left (2 \, d x + 2 \, c\right )} + a + 2 \, b}{2 \, \sqrt {-a b - b^{2}}}\right )}{{\left (a^{2} + a b\right )} \sqrt {-a b - b^{2}}} - \frac {d x + c}{a} + \frac {2}{{\left (a + b\right )} {\left (e^{\left (2 \, d x + 2 \, c\right )} - 1\right )}}}{d} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________