be an indefinite integral or antiderivative of
where x = g (u)
is a substitution. Accordingly, the inverse function
u = g −1(x)
describes the dependence of the new variable on the old variable.
It's important to remember that the differential dx
also needs to be substituted. It must be replaced with
the differential of the new variable du.
For definite integrals, it is also necessary to change the limits of integration.
See about this on the page "The Definite Integral and Fundamental Theorem of