Is there an inverse chain rule for integration?
Integration by substitution is the inverse of differentiation using the chain rule.
A different way to see this is to do n integration by substitution and then check the answer by differentiation.
Now, if we check our answer by differentiating, we will use the chain rule.
We could also write the integration using
# = int (g(x))^(1/2) g'(x)dx = 2/3(g(x))^(3/2)+C#