Integral of the function: $f(r,n,x)=[J_0(x)]^nJ_1(rx)$

Question

In a paper of Kluyver related to the topics of random distribuited vectors with random phase and length, the following integral has to be evaluated: $$P(r,n)=\int_0^\infty[J_0(x)]^nJ_1(rx)dx$$ with $n\in\mathbb{N},r\in\mathbb{R}$. It's possible to have a closed form solution for $n=1$ and $n=2$. My question is: is it possible to evaluate this integral in closed form for any $n$? I tried to put $y=rx$ and integrate by parts, but the method seems to be uneffective. Is it another way to evaluate it? Thanks.