From Folland Abstract Harmonic Analysis - Why is $\int f(x \xi) d\xi = \int f(x \xi^{-1}) \Delta_H(\xi^{-1}) d \xi$?
This is on page 57.
Here is the notation:
$H$ is a closed subgroup of a locally compact, Hausdorff group $G$. $d \xi$ is the left Haar measure on $H$. $\Delta_H$ is the modular function.
I know that $\Delta_H(x^{-1}) d \xi$ is the right invariant Haar measure $(d\xi)(E^{-1})$ (or however I should notate that). I am sure that this is part of it, but I can't finish the substitution - I am very bad at calculus, unfortunately. Please help. (Also I'm feeling super lazy right now, but want to get past this point in the book. There, full disclosure.)