Q$4(10$ points$)$

In the following question, we will solve

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}sin(x)e^{x}dx$

Let $u=sin(x)$ and $dv=e^x$ and perform one iteration of integration by parts.

Let $u=cos(x)$ and $dv=e^x$ and perform another iteration of integration by parts.

Let $I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}sin(x)e^{x}dx.$ Use part $(1)$ and $(2)$ to solve for I.