When I integrate $\sin(π/x^2)$ on W|A, I get:
\begin{equation} \int \sin\left(\frac{π}{x^2} \right)\:dx = x\sin\left(\frac{\pi}{x^2}\right) - \sqrt{2}\pi C\left( \frac{\sqrt{2}}{x} \right) + D \end{equation}
Where $D$ is the constant of integration and $C(x)$ is the Fresnel C Integral.
But I have no idea how to prove this! There is no general integration formula for composite formulas, and the answer on W|A needs proof (there is no step-by-step and to me, it looks kind of shady. http://mathworld.wolfram.com/FresnelIntegrals.html is about the Fresnel C integral. I have found no resources anywhere and I need help with the proof!
Can anyone provide some starting points / tips?