I am trying to do the following integral for a few days now, but getting nowhere.
\begin{align} \int_0^x \mathrm dy\,y^2 \cos(y^2) C^2 \!\!\left(\!\dfrac{\sqrt{2}\,y}{\sqrt\pi}\!\right)\! \end{align}
In reality only the first one is causing me troubles, however I have pasted the entire expression as it might lead to some cancellations. Any help would be welcome. $C()$ is the Fresnel integral.