We recall that the Airy function is (well) defined by:
$\text{Ai}(x) = \frac{1}{\pi} \int_0^\infty \cos\left(\frac{t^3}{3} + xt\right) dt$
I want to apply the theorem of differentiation under the integral sign (Leibniz rule), but I can't find the dominating functions.
The derivative we consider is given by $ -((t + x^2) \sin(tx + \frac{x^3}{3})) $.