\[ \int \frac {1}{\sqrt {-x} \sqrt {2-b x} \sqrt {2+b x}} \, dx \]
Optimal antiderivative \[ -\frac {\EllipticF \left (\frac {\sqrt {b}\, \sqrt {-x}\, \sqrt {2}}{2}, i\right ) \sqrt {2}}{\sqrt {b}} \]
command
integrate(1/(-x)^(1/2)/(-b*x+2)^(1/2)/(b*x+2)^(1/2),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \frac {2 \, {\rm weierstrassPInverse}\left (\frac {16}{b^{2}}, 0, x\right )}{b} \]
Fricas 1.3.7 via sagemath 9.3 output
\[ {\rm integral}\left (\frac {\sqrt {b x + 2} \sqrt {-b x + 2} \sqrt {-x}}{b^{2} x^{3} - 4 \, x}, x\right ) \]