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