Integral of Bessel function

1. Aug 11, 2014

grepecs

1. The problem statement, all variables and given/known data

I've been given that the Bessel function

∫(J3/2(x)/x2)dx=1/2π (the integral goes from 0 to infinity).

2. Relevant equations

∫(J3/2(ax)/x2)dx,

where a is a constant.

3. The attempt at a solution

Is the following correct?

a2∫(J3/2(ax)/(ax)2)dx=a2/2π

(This is just a part of a triple integral. We are not asked nor expected to bother too much with the Bessel function, since it is not the focus of the problem).

2. Aug 11, 2014

dextercioby

No, I think one of the 'a's goes away. Do the substitution again: y = ax. With a>0.

3. Aug 11, 2014

grepecs

Oh, of course. I then get dx=dy/a, which solves the problem for me. Thanks!