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