Let X and Y be two random variables with joint density function f_XY. Compute the pdf of U = XY.

Here is my work.

U=XY and V=X so X=V and Y=U/V

f_U(u) = integral (-inf to inf)f_U(u)dv = integral (-inf to inf)(f_XY(v,u/v)dv

Apparently my answer is off by a factor of 1/|v| (which just happens to be |Jacobian|). I just don't see where 1/|v| comes from.

Please advise me on this.

Thanks!