Mark the correct alternative in each of the following:

let $\mathrm{I}=\int e^{x}\left(f(x)+f^{\prime}(x)\right) \mathrm{d}_{x}$

Open the brackets, we get

$I=\left\{\int e^{x} f(x) d x+\int e^{x} f^{\prime}(x) d x\right\}$

$=U+\int e^{x} f^{\prime}(x) d x$

$U=\int e^{x} f(x) d x$

To solve $U$ using integration by parts

$U=f(x) \int e^{x} d x-\int\left[f^{\prime}(x) \int e^{x}\right]$

$=f(x) e^{x}-\int f^{\prime}(x) e^{x}$

$=U+\int e^{x} f^{\prime}(x) d x$

$I=e^{x} f(x)+\int f^{\prime}(x) e^{x} d x-\int e^{x} f^{\prime}(x) d x$

$I=e^{x} f(x)+c$