I've to find the Laplace transform of a voltage signal:
$$\text{U}\left(t\right)=\left|\hat{\text{u}}\sin\left(\omega t+\varphi\right)\right|=\left|\hat{\text{u}}\right|\sqrt{\sin^2\left(\omega t+\varphi\right)}$$
Where all the variables are real numbers.
So, we get:
$$\int_0^\infty e^{-\text{s}t}\cdot\left|\hat{\text{u}}\sin\left(\omega t+\varphi\right)\right|\space\text{d}t=\left|\hat{\text{u}}\right|\int_0^\infty e^{-\text{s}t}\cdot\sqrt{\sin^2\left(\omega t+\varphi\right)}\space\text{d}t=$$ $$\frac{\left|\hat{\text{u}}\right|}{\sqrt{2}}\int_0^\infty e^{-\text{s}t}\cdot\sqrt{1-\cos\left(2\omega t+2\varphi\right)}\space\text{d}t$$