I How can the integral be rewritten using a change of variables?

[Lapidus]

Here http://www.damtp.cam.ac.uk/user/db275/Cosmology/Lectures.pdf, I find on page 31 in (2.1.5)

I assume that it is childish calculus that connects both sides of this equation. But still, can someone help me why the integral can be rewritten like that?

thanks!

 

[Orodruin]

It is a standard change of variables.

$\int f(a(t)) dt = \int f(a) (dt/da) da$