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