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