\[ \int \frac {\text {sech}^3(c+d x)}{a+i a \sinh (c+d x)} \, dx \]
Optimal antiderivative \[ \frac {3 \arctan \! \left (\sinh \! \left (d x +c \right )\right )}{8 a d}-\frac {\mathrm {I}}{8 d \left (a -\mathrm {I} a \sinh \! \left (d x +c \right )\right )}+\frac {\mathrm {I} a}{8 d \left (a +\mathrm {I} a \sinh \! \left (d x +c \right )\right )^{2}}+\frac {\mathrm {I}}{4 d \left (a +\mathrm {I} a \sinh \! \left (d x +c \right )\right )} \]
command
integrate(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
\[ -\frac {8 \, {\left (3 \, e^{\left (-d x - c\right )} - 6 i \, e^{\left (-2 \, d x - 2 \, c\right )} + 2 \, e^{\left (-3 \, d x - 3 \, c\right )} + 6 i \, e^{\left (-4 \, d x - 4 \, c\right )} + 3 \, e^{\left (-5 \, d x - 5 \, c\right )}\right )}}{{\left (64 i \, a e^{\left (-d x - c\right )} - 32 \, a e^{\left (-2 \, d x - 2 \, c\right )} + 128 i \, a e^{\left (-3 \, d x - 3 \, c\right )} + 32 \, a e^{\left (-4 \, d x - 4 \, c\right )} + 64 i \, a e^{\left (-5 \, d x - 5 \, c\right )} + 32 \, a e^{\left (-6 \, d x - 6 \, c\right )} - 32 \, a\right )} d} - \frac {3 i \, \log \left (e^{\left (-d x - c\right )} + i\right )}{8 \, a d} + \frac {3 i \, \log \left (e^{\left (-d x - c\right )} - i\right )}{8 \, a d} \]