Find the leading order approximation to the integral \begin{equation} I=\int _0^\infty \cos x(t^3/3-t)\,dt \end{equation} for large positive \(x\).
Hint: Use that \[ \int _{-\infty }^{\infty }\cos at^2\,dt =\int _{-\infty }^{\infty }\sin at^2\,dt =\sqrt {\frac {\pi }{2a}}. \]