\[ \int \frac {\tanh (c+d x)}{\left (a+b \text {sech}^2(c+d x)\right )^3} \, dx \]
Optimal antiderivative \[ -\frac {b^{2}}{4 a^{3} d \left (b +a \left (\cosh ^{2}\left (d x +c \right )\right )\right )^{2}}+\frac {b}{a^{3} d \left (b +a \left (\cosh ^{2}\left (d x +c \right )\right )\right )}+\frac {\ln \! \left (b +a \left (\cosh ^{2}\left (d x +c \right )\right )\right )}{2 a^{3} d} \]
command
integrate(tanh(d*x+c)/(a+b*sech(d*x+c)^2)^3,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
\[ -\frac {\frac {4 \, d x}{a^{3}} - \frac {2 \, \log \left (a e^{\left (4 \, d x + 4 \, c\right )} + 2 \, a e^{\left (2 \, d x + 2 \, c\right )} + 4 \, b e^{\left (2 \, d x + 2 \, c\right )} + a\right )}{a^{3}} + \frac {3 \, a e^{\left (8 \, d x + 8 \, c\right )} + 12 \, a e^{\left (6 \, d x + 6 \, c\right )} + 8 \, b e^{\left (6 \, d x + 6 \, c\right )} + 18 \, a e^{\left (4 \, d x + 4 \, c\right )} + 16 \, b e^{\left (4 \, d x + 4 \, c\right )} + 12 \, a e^{\left (2 \, d x + 2 \, c\right )} + 8 \, b e^{\left (2 \, d x + 2 \, c\right )} + 3 \, a}{{\left (a e^{\left (4 \, d x + 4 \, c\right )} + 2 \, a e^{\left (2 \, d x + 2 \, c\right )} + 4 \, b e^{\left (2 \, d x + 2 \, c\right )} + a\right )}^{2} a^{2}}}{4 \, d} \]