\[ \int \text {sech}^{\frac {3}{2}}(a+b x) \, dx \]
Optimal antiderivative \[ \frac {2 \sinh \left (b x +a \right ) \sqrt {\mathrm {sech}\left (b x +a \right )}}{b}+\frac {2 i \sqrt {\frac {\cosh \left (b x +a \right )}{2}+\frac {1}{2}}\, \EllipticE \left (i \sinh \left (\frac {a}{2}+\frac {b x}{2}\right ), \sqrt {2}\right ) \left (\sqrt {\cosh }\left (b x +a \right )\right ) \sqrt {\mathrm {sech}\left (b x +a \right )}}{\cosh \left (\frac {a}{2}+\frac {b x}{2}\right ) b} \]
command
integrate(sech(b*x+a)^(3/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\left (\sqrt {2} \sqrt {\frac {\cosh \left (b x + a\right ) + \sinh \left (b x + a\right )}{\cosh \left (b x + a\right )^{2} + 2 \, \cosh \left (b x + a\right ) \sinh \left (b x + a\right ) + \sinh \left (b x + a\right )^{2} + 1}} {\left (\cosh \left (b x + a\right ) + \sinh \left (b x + a\right )\right )} + \sqrt {2} {\rm weierstrassZeta}\left (-4, 0, {\rm weierstrassPInverse}\left (-4, 0, \cosh \left (b x + a\right ) + \sinh \left (b x + a\right )\right )\right )\right )}}{b} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\operatorname {sech}\left (b x + a\right )^{\frac {3}{2}}, x\right ) \]