I have an integral which I am supposed to solve numerically and can find an approximated answer to it. The integral in question is
$$\int_{-\infty}^{\infty}\sin^2{\frac1{x}} \, \mathrm{d}x=\pi~.$$
I have check numerous sources but cannot find an analytical approach to the integral. Possibly there is a neat trick using a residual or something which I cannot see, but I am out of luck.
If someone have noticed a way to find an exact answer, I would definitely appreciate it.