\[ \int \frac {1}{\sqrt {2-2 x^2} \sqrt {1-x^2}} \, dx \]
Optimal antiderivative \[ \frac {\arctanh \! \left (x \right ) \sqrt {2}}{2} \]
command
integrate(1/(-2*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \frac {1}{4} \, \sqrt {2} \log \left (x + 1\right ) - \frac {1}{4} \, \sqrt {2} \log \left (x - 1\right ) \]