Evaluate the integral $\int \sin(x)\cos(3x^2)dx$ I am looking for a solution for the following integral problem.
$$\int \sin(x)\cos(3x^2)dx$$
Passed over these integral things long time ago. I cannot see how to go for a solution. 


$$\begin{align}I=\dfrac12~\sqrt{\dfrac\pi6}~\bigg\{\cos\dfrac1{12}\bigg[S\bigg(\dfrac{6x+1}{\sqrt{6\pi}}\bigg)-S\bigg(\dfrac{6x-1}{\sqrt{6\pi}}\bigg)\bigg]+\\\\+\sin\dfrac1{12}\bigg[C\bigg(\dfrac{6x-1}{\sqrt{6\pi}}\bigg)-C\bigg(\dfrac{6x+1}{\sqrt{6\pi}}\bigg)\bigg]\bigg\}\end{align}$$

where S and C are the two Fresnel integrals.
