Let $\int e^x\left\{f(x)-f'(x)\right\} d x=\phi(x)$. Then, $\int e^x f(x) d x$ is equal to
Answer & explanation
Correct answer: option 3
We know that
$\int e^x\left\{f(x)+f'(x)\right\} d x=e^x f(x)$
It is given that
$\int e^x\left\{f(x)-f'(x)\right\} d x=\phi(x)$
Adding these two, we get
$2 \int e^x f(x) d x=\phi(x)+e^x f(x)$
$\int e^x f(x) d x=\frac{1}{2}\left\{\phi(x)+e^x f(x)\right\}$