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