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