I need to find laplace transform for this $ℒ_t[\sqrt{\sin(2 t) + 1}]$

Question

if $f(t) = \sqrt{\sin(2 t) + 1}>> I$ need to solve this problem and find Laplace transform for it $( ℒ_t[f(t)] = ??)$

Answer 1

Notice that $$ \sin 2t +1 = 2 \sin t \cos t + \sin^2 t + \cos ^2 t = ( \sin t + \cos t )^2$$

That takes care of the square root and the rest is easy and you can manage it.