Question
Evaluate: $\int e^x\left[\frac{\sqrt{1-x^2} \sin ^{-1} x+1}{\sqrt{1-x^2}}\right] d x$
$\begin{aligned} & \int e^x\left[\frac{\sqrt{1-x^2} \sin ^{-1} x+1}{\sqrt{1-x^2}}\right] d x \\ & =\int e^x\left[\sin ^{-1} x+\frac{1}{\sqrt{1-x^2}}\right] d x\end{aligned}$
$\begin{aligned} & \text { We know that } \int e^x[f(x)+f \prime(x)] d x=e^x \cdot f(x)+c \\ & =e^x \cdot \sin ^{-1} x+c\end{aligned}$
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