Negative moments of a functional of Wiener process

Question

At the moment I am reading D. Nualart's The Malliavin Calculus and Related Topics. The problem I am trying to solve is the following: Show that the random variable $\int_0^1 s^2\arctan W_s\, ds$ posssesses a $C^\infty$ density, here $W_s$ stands for a Wiener process. After applying results from the corresponding chapter of the book, it is left to verify the following: for all $p\geq 1$ $E[(\int_0^1\frac{s^3}{1+W^2_s}\, ds)^{-2p}]<\infty$. How can I do it? (In fact, I am not familiar with any result concerning negative moments of r.vs, except of a few problems in M. Yor, L. Chaumont ``Excercise in probability'')