integration - Solve $intfrac{e^x.(2-x^2)}{(1-x)sqrt{1-x^2}}dx$

Evaluate the integral $$\int\frac{e^x.(2-x^2)}{(1-x)\sqrt{1-x^2}}dx$$

Set $u=\dfrac{1}{\sqrt{1-x}}\implies du=\dfrac{-dx}{2(1-x)^{3/2}}$
$$
\int\frac{e^x.(2-x^2)}{(1-x)\sqrt{1-x^2}}dx=\int\frac{e^x.(2-x^2)}{(1-x)^{3/2}\sqrt{1+x}}dx=\int\frac{e^x{2-x^2}.-2du}{\sqrt{\dfrac{2t^2-1}{t^2}}}dx
$$
I have no clue about what is the easiest substitution possible inorder to solve the above integral ?

I tried $u=\dfrac{1}{\sqrt{1-x}}$ yet it is becoming more cumbersome I guess.