\[ \int \frac {\text {csch}^3(c+d x)}{a+b \tanh ^2(c+d x)} \, dx \]
Optimal antiderivative \[ \frac {\left (a +2 b \right ) \arctanh \! \left (\cosh \! \left (d x +c \right )\right )}{2 a^{2} d}-\frac {\coth \! \left (d x +c \right ) \mathrm {csch}\! \left (d x +c \right )}{2 a d}-\frac {\arctanh \! \left (\frac {\mathrm {sech}\left (d x +c \right ) \sqrt {b}}{\sqrt {a +b}}\right ) \sqrt {b}\, \sqrt {a +b}}{a^{2} d} \]
command
integrate(csch(d*x+c)^3/(a+b*tanh(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
\[ \frac {\frac {2 \, {\left (3 \, a b - b^{2} - \sqrt {-a b} {\left (a - 3 \, b\right )}\right )} {\left | a e^{\left (2 \, c\right )} + b e^{\left (2 \, c\right )} \right |} \arctan \left (\frac {e^{\left (d x\right )}}{\sqrt {\frac {a^{3} e^{\left (2 \, c\right )} - a^{2} b e^{\left (2 \, c\right )} + \sqrt {{\left (a^{3} e^{\left (2 \, c\right )} - a^{2} b e^{\left (2 \, c\right )}\right )}^{2} - {\left (a^{3} e^{\left (4 \, c\right )} + a^{2} b e^{\left (4 \, c\right )}\right )} {\left (a^{3} + a^{2} b\right )}}}{a^{3} e^{\left (4 \, c\right )} + a^{2} b e^{\left (4 \, c\right )}}}}\right ) e^{\left (-2 \, c\right )}}{{\left (a^{3} - a^{2} b + 2 \, \sqrt {-a b} a^{2}\right )} \sqrt {a^{2} - b^{2} + 2 \, \sqrt {-a b} {\left (a + b\right )}}} + \frac {2 \, {\left (3 \, a b - b^{2} + \sqrt {-a b} {\left (a - 3 \, b\right )}\right )} {\left | a e^{\left (2 \, c\right )} + b e^{\left (2 \, c\right )} \right |} \arctan \left (\frac {e^{\left (d x\right )}}{\sqrt {\frac {a^{3} e^{\left (2 \, c\right )} - a^{2} b e^{\left (2 \, c\right )} - \sqrt {{\left (a^{3} e^{\left (2 \, c\right )} - a^{2} b e^{\left (2 \, c\right )}\right )}^{2} - {\left (a^{3} e^{\left (4 \, c\right )} + a^{2} b e^{\left (4 \, c\right )}\right )} {\left (a^{3} + a^{2} b\right )}}}{a^{3} e^{\left (4 \, c\right )} + a^{2} b e^{\left (4 \, c\right )}}}}\right ) e^{\left (-2 \, c\right )}}{{\left (a^{3} - a^{2} b - 2 \, \sqrt {-a b} a^{2}\right )} \sqrt {a^{2} - b^{2} - 2 \, \sqrt {-a b} {\left (a + b\right )}}} + \frac {{\left (a e^{c} + 2 \, b e^{c}\right )} e^{\left (-c\right )} \log \left (e^{\left (d x + c\right )} + 1\right )}{a^{2}} - \frac {{\left (a e^{c} + 2 \, b e^{c}\right )} e^{\left (-c\right )} \log \left ({\left | e^{\left (d x + c\right )} - 1 \right |}\right )}{a^{2}} - \frac {2 \, {\left (e^{\left (3 \, d x + 3 \, c\right )} + e^{\left (d x + c\right )}\right )}}{a {\left (e^{\left (2 \, d x + 2 \, c\right )} - 1\right )}^{2}}}{2 \, d} \]