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

$\phi(x)+e^x f(x)$ $\phi(x)-e^x f(x)$ $\frac{1}{2}\left\{\phi(x)+e^x f(x)\right\}$ $\frac{1}{2}\left\{\phi(x)+e^x f'(x)\right\}$

$\frac{1}{2}\left\{\phi(x)+e^x f(x)\right\}$

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 $2 \int e^x f(x) d x=\phi(x)+e^x f(x)$ $\int e^x f(x) d x=\frac{1}{2}\left\{\phi(x)+e^x f(x)\right\}$