\[ \int \frac {(e+f x)^3 \text {sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx \]
Optimal antiderivative \[ -\frac {\mathrm {I} f \left (f x +e \right )^{2} \tanh \! \left (d x +c \right )}{2 a \,d^{2}}-\frac {5 f^{2} \left (f x +e \right ) \arctan \! \left ({\mathrm e}^{d x +c}\right )}{a \,d^{3}}+\frac {3 \left (f x +e \right )^{3} \arctan \! \left ({\mathrm e}^{d x +c}\right )}{4 a d}-\frac {9 \,\mathrm {I} f \left (f x +e \right )^{2} \polylog \! \left (2, \mathrm {-I} \,{\mathrm e}^{d x +c}\right )}{8 a \,d^{2}}-\frac {\mathrm {I} f \left (f x +e \right )^{2} \mathrm {sech}\! \left (d x +c \right )^{2} \tanh \! \left (d x +c \right )}{4 a \,d^{2}}-\frac {\mathrm {I} f^{2} \left (f x +e \right ) \mathrm {sech}\! \left (d x +c \right )^{2}}{4 a \,d^{3}}-\frac {5 \,\mathrm {I} f^{3} \polylog \! \left (2, \mathrm {I} \,{\mathrm e}^{d x +c}\right )}{2 a \,d^{4}}+\frac {9 \,\mathrm {I} f \left (f x +e \right )^{2} \polylog \! \left (2, \mathrm {I} \,{\mathrm e}^{d x +c}\right )}{8 a \,d^{2}}+\frac {5 \,\mathrm {I} f^{3} \polylog \! \left (2, \mathrm {-I} \,{\mathrm e}^{d x +c}\right )}{2 a \,d^{4}}-\frac {9 \,\mathrm {I} f^{2} \left (f x +e \right ) \polylog \! \left (3, \mathrm {I} \,{\mathrm e}^{d x +c}\right )}{4 a \,d^{3}}+\frac {9 \,\mathrm {I} f^{2} \left (f x +e \right ) \polylog \! \left (3, \mathrm {-I} \,{\mathrm e}^{d x +c}\right )}{4 a \,d^{3}}+\frac {9 \,\mathrm {I} f^{3} \polylog \! \left (4, \mathrm {I} \,{\mathrm e}^{d x +c}\right )}{4 a \,d^{4}}+\frac {\mathrm {I} f^{2} \left (f x +e \right ) \ln \! \left (1+{\mathrm e}^{2 d x +2 c}\right )}{a \,d^{3}}-\frac {f^{3} \mathrm {sech}\! \left (d x +c \right )}{4 a \,d^{4}}+\frac {9 f \left (f x +e \right )^{2} \mathrm {sech}\! \left (d x +c \right )}{8 a \,d^{2}}-\frac {9 \,\mathrm {I} f^{3} \polylog \! \left (4, \mathrm {-I} \,{\mathrm e}^{d x +c}\right )}{4 a \,d^{4}}+\frac {f \left (f x +e \right )^{2} \mathrm {sech}\! \left (d x +c \right )^{3}}{4 a \,d^{2}}-\frac {\mathrm {I} f \left (f x +e \right )^{2}}{2 a \,d^{2}}+\frac {\mathrm {I} \left (f x +e \right )^{3} \mathrm {sech}\! \left (d x +c \right )^{4}}{4 a d}+\frac {\mathrm {I} f^{3} \tanh \! \left (d x +c \right )}{4 a \,d^{4}}-\frac {f^{2} \left (f x +e \right ) \mathrm {sech}\! \left (d x +c \right ) \tanh \! \left (d x +c \right )}{4 a \,d^{3}}+\frac {3 \left (f x +e \right )^{3} \mathrm {sech}\! \left (d x +c \right ) \tanh \! \left (d x +c \right )}{8 a d}+\frac {\mathrm {I} f^{3} \polylog \! \left (2, -{\mathrm e}^{2 d x +2 c}\right )}{2 a \,d^{4}}+\frac {\left (f x +e \right )^{3} \mathrm {sech}\! \left (d x +c \right )^{3} \tanh \! \left (d x +c \right )}{4 a d} \]
command
integrate((f*x+e)^3*sech(d*x+c)^3/(a+I*a*sinh(d*x+c)),x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \text {Exception raised: RuntimeError} \]
Maxima 5.44 via sagemath 9.3 output
\[ \text {output too large to display} \]