$\int e^x \bigg( \sin ^{-1} x +\large\frac{1}{\sqrt {1-x^2}}\bigg) dx $
=> $ \int e^x . \sin ^{-1} x dx + e^x. \large\frac{1}{\sqrt {1-x^2}}$$dx$
=> $\sin ^{-1}x.e^x -\int \large\frac{1}{\sqrt {1+x^2}}$$ \times e^x dx \int e^x \times \large\frac{1}{\sqrt {1-x^2}}$$dx$
$e^x \sin ^{-1} x +c$
Hence a is the correct answer.