If $\int g(x) d x=g(x)$, then the value of the integral $\int f(x) g(x)\left\{f(x)+2 f'(x)\right\} d x$, is

$f(x) g(x)+C$ $\{f(x)\}^2 g(x)+C$ $\left\{f(x)-f'(x)\right\} g(x)+C$ $\{f(x)\}^2 g'(x)+C$

$\{f(x)\}^2 g(x)+C$

Let $I=\int f(x) g(x)\left\{f(x)+2 f'(x)\right\} d x$ $\Rightarrow I=\int\{f(x)\}^2 g(x) d x+\int 2 f(x) f'(x) g(x) d x$ $\Rightarrow I=\{f(x)\}^2\left\{\int g(x) d x\right\}- 2 f(x) f'(x) g(x) d x +\int 2 f(x) f'(x) g(x) d x+C$ $\Rightarrow I=\{f(x)\}^2 g(x)+C$