Computation of a functional for large values

Question

Consider the following function :

$$f(x) = \sin^2(\frac{π\Gamma(x)}{2x})$$

Now consider the following functional :

$$I(x)=\int_0^\infty \frac{f(x + iy) − f(x − iy)}{e^{2πy}-1} dy$$

I need values for of $I(x)$ for large $x$ at least upto 10^2.

I tried it on Mathematica but I couldn't .

Here are some calculated values for small X's :img1 img2

Also if possible , what is the apparent asymptotic of minimas and Maximas of the functional?