I need to prove that the following integral converges
int ( sqrt(x) * cos(x^2) dx , x = 0 to infinity )
Using Wolfram I found that the solution can be expressed in the closed form
(1/4) * sqrt ( 1 - sqrt(2) ) * Gamma ( 3 / 4 )
Whilst I don't have to show the exact result, I am completely lost with showing that it converges.
Any starting points/ hints would be greatly appreciated,