Not so standard

Evaluate: $\int \limits_0^\infty ( 2 + f(x) )(1- f(x) ) \frac{ \text{d}x}{x^2}$ where, $\displaystyle f(x) = \frac{ \sin x }{x}$.

The value of the integral can be expressed as $\displaystyle \frac{a \pi ^b }{c}$.

Given $a$ and $c$ are coprime, submit the value of $a+ b+ c$.

Details and Assumptions:
Following integrals may be helpful:

• $\displaystyle \int \limits_0^\infty \big( f(x) \big)^2 \text{d}x = \frac{ \pi }{2}$

• $\displaystyle \int \limits_0^\infty \big( f(x) \big)^3 \text{d}x = \frac{3 \pi }{8}$

• $\displaystyle \int \limits_0^\infty \big( f(x) \big)^4 \text{d}x = \frac{ \pi }{3}$