Question

$\int \frac{e^{m{\sin }^{-1}x}}{\sqrt{1-x^2}}dx$

Answer 1

$$\begin{gathered} \int \frac{e^{m{\sin }^{-1}x}}{\sqrt{1-x^2}}dx \\ \mathrm{Let}{\sin }^{-1}x=t \\ \Rightarrow \frac{1}{\sqrt{1-x^2}}dx=dt \\ \mathrm{Now},\int \frac{e^{m{\sin }^{-1}x}}{\sqrt{1-x^2}}dx \\ =\int e^{mt}·dt \\ =\frac{e^{mt}}{m}+C \\ =\frac{e^{m{\sin }^{-1}x}}{m}+C \end{gathered}$$