# 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!