How to prove $\int_0^{\infty}e^{-sx}\frac{\sin(x)^2}{x}dx = \frac{1}{4}\ln(1- \frac{4}{s^2})$ using Tonelli-Fubini

I need some help with in trying to prove that$$\int_{0}^{\infty}{\rm e}^{-sx}\,\frac{\sin^{2}(x)}{x}\,{\rm d}x = \frac{1}{4}\ln\left(1- \frac{4}{s^{2}}\right)\quad\mbox{using}\ Tonelli\mbox{--}Fubini$$Now, by Tonelli-Fubini we have that :$$\int_0^{\infty}\int_0^1 e^{-sx}{\sin(2xy)}dydx = \int_0^1\int_0^{\infty}e^{-sx}{\sin(2xy)}dxdy$$After some calculation, we find that$$\int_0^{\infty}\int_0^1 e^{-sx}{\sin(2xy)}dydx = \int_0^{\infty}e^{-sx}\frac{\sin(x)^2}{x}dx$$$$\mbox{Now we need to prove that}\\int_0^1\int_0^{\infty}e^{-sx}{\sin(2xy)}dxdy =\frac{1}{4}\ln\left(1- \frac{4}{s^2}\right)$$

This is when I need help : How can I show this equality? I have been thinking but I cannot come up with anything. I will appreciate some help.