\[ \int \frac {1}{\sqrt {b \sinh (c+d x)}} \, dx \]
Optimal antiderivative \[ \frac {2 i \sqrt {\frac {1}{2}+\frac {\sin \left (i d x +i c \right )}{2}}\, \EllipticF \left (\cos \left (\frac {1}{2} i c +\frac {1}{4} \pi +\frac {1}{2} i d x \right ), \sqrt {2}\right ) \sqrt {i \sinh \left (d x +c \right )}}{\sin \left (\frac {1}{2} i c +\frac {1}{4} \pi +\frac {1}{2} i d x \right ) d \sqrt {b \sinh \left (d x +c \right )}} \]
command
integrate(1/(b*sinh(d*x+c))^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, \sqrt {2} {\rm weierstrassPInverse}\left (4, 0, \cosh \left (d x + c\right ) + \sinh \left (d x + c\right )\right )}{\sqrt {b} d} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {b \sinh \left (d x + c\right )}}{b \sinh \left (d x + c\right )}, x\right ) \]