\[ \int \frac {\sqrt {1-x^2}+x \text {ArcSin}(x)}{\text {ArcSin}(x)-x^2 \text {ArcSin}(x)} \, dx \]
Optimal antiderivative \[ -\frac {\ln \! \left (-x^{2}+1\right )}{2}+\ln \! \left (\arcsin \! \left (x \right )\right ) \]
command
integrate((x*asin(x)+(-x**2+1)**(1/2))/(asin(x)-x**2*asin(x)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \int \frac {\sqrt {1 - x^{2}}}{x^{2} \operatorname {asin}{\left (x \right )} - \operatorname {asin}{\left (x \right )}}\, dx - \int \frac {x \operatorname {asin}{\left (x \right )}}{x^{2} \operatorname {asin}{\left (x \right )} - \operatorname {asin}{\left (x \right )}}\, dx \]
Sympy 1.8 under Python 3.8.8 output
\[ - \frac {\log {\left (2 x^{2} - 2 \right )}}{2} + \log {\left (\operatorname {asin}{\left (x \right )} \right )} \]