\[ \int e^{\coth ^{-1}(x)} \sqrt {1-x} \, dx \]
Optimal antiderivative \[ \frac {2 \left (1+x \right ) \sqrt {1-x}}{3 \sqrt {\frac {-1+x}{1+x}}} \]
command
integrate(1/((-1+x)/(1+x))**(1/2)*(1-x)**(1/2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \int \frac {\sqrt {1 - x}}{\sqrt {\frac {x - 1}{x + 1}}}\, dx \]
Sympy 1.8 under Python 3.8.8 output
\[ - \frac {2 i x}{3 \sqrt {\frac {1}{x + 1}}} - \frac {2 i}{3 \sqrt {\frac {1}{x + 1}}} \]