Integrating J₃/₂(ax)/x² with a constant scaling factor

[grepecs]

Homework Statement

I've been given that the Bessel function

∫(J_3/2(x)/x²)dx=1/2π (the integral goes from 0 to infinity).

Homework Equations

∫(J_3/2(ax)/x²)dx,

where a is a constant.

The Attempt at a Solution

Is the following correct?

a²∫(J_3/2(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).

 

[dextercioby]

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

 

[grepecs]

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

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