I have been working on an integral for a few days without getting anywhere. I was wondering if anyone could help:
\begin{align}
&\int_0^x dy\,y^2 \cos(y^2) C^2 \!\!\left(\!\frac{\sqrt{2}\,y}{\sqrt\pi}\!\right)
\end{align}
C() is the Fresnel cosine integral. In reality only the first integral is causing troubles, but I have posted all of them since cancellations may occur. I have tried many integrations by part, but none of them worked. I posted this here as I assumed Fresnel integrals are post-calculus, but please do move the thread if you find it necessary.
\begin{align}
&\int_0^x dy\,y^2 \cos(y^2) C^2 \!\!\left(\!\frac{\sqrt{2}\,y}{\sqrt\pi}\!\right)
\end{align}
C() is the Fresnel cosine integral. In reality only the first integral is causing troubles, but I have posted all of them since cancellations may occur. I have tried many integrations by part, but none of them worked. I posted this here as I assumed Fresnel integrals are post-calculus, but please do move the thread if you find it necessary.
Last edited: