\[ \int \frac {\coth ^3(c+d x)}{\left (a+b \text {sech}^2(c+d x)\right )^2} \, dx \]
Optimal antiderivative \[ \frac {b^{3}}{2 a^{2} \left (a +b \right )^{2} d \left (b +a \left (\cosh ^{2}\left (d x +c \right )\right )\right )}-\frac {\mathrm {csch}\! \left (d x +c \right )^{2}}{2 \left (a +b \right )^{2} d}+\frac {b^{2} \left (3 a +b \right ) \ln \! \left (b +a \left (\cosh ^{2}\left (d x +c \right )\right )\right )}{2 a^{2} \left (a +b \right )^{3} d}+\frac {\left (a +3 b \right ) \ln \! \left (\sinh \! \left (d x +c \right )\right )}{\left (a +b \right )^{3} d} \]
command
integrate(coth(d*x+c)^3/(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
\[ \frac {\frac {{\left (3 \, a b^{2} + b^{3}\right )} \log \left (a e^{\left (4 \, d x + 4 \, c\right )} + 2 \, a e^{\left (2 \, d x + 2 \, c\right )} + 4 \, b e^{\left (2 \, d x + 2 \, c\right )} + a\right )}{a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}} + \frac {2 \, {\left (a e^{\left (2 \, c\right )} + 3 \, b e^{\left (2 \, c\right )}\right )} \log \left ({\left | -e^{\left (2 \, d x + 2 \, c\right )} + 1 \right |}\right )}{a^{3} e^{\left (2 \, c\right )} + 3 \, a^{2} b e^{\left (2 \, c\right )} + 3 \, a b^{2} e^{\left (2 \, c\right )} + b^{3} e^{\left (2 \, c\right )}} - \frac {2 \, d x}{a^{2}} - \frac {3 \, a b^{2} e^{\left (4 \, d x + 4 \, c\right )} + b^{3} e^{\left (4 \, d x + 4 \, c\right )} + 6 \, a b^{2} e^{\left (2 \, d x + 2 \, c\right )} + 10 \, b^{3} e^{\left (2 \, d x + 2 \, c\right )} + 3 \, a b^{2} + b^{3}}{{\left (a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right )} {\left (a e^{\left (4 \, d x + 4 \, c\right )} + 2 \, a e^{\left (2 \, d x + 2 \, c\right )} + 4 \, b e^{\left (2 \, d x + 2 \, c\right )} + a\right )}} - \frac {3 \, a e^{\left (4 \, d x + 4 \, c\right )} + 9 \, b e^{\left (4 \, d x + 4 \, c\right )} - 2 \, a e^{\left (2 \, d x + 2 \, c\right )} - 14 \, b e^{\left (2 \, d x + 2 \, c\right )} + 3 \, a + 9 \, b}{{\left (a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right )} {\left (e^{\left (2 \, d x + 2 \, c\right )} - 1\right )}^{2}}}{2 \, d} \]