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