# Indefinite Integrals

### Topics

**Integration by substitution** is a way of undoing the chain rule. This is a once-in-a-lifetime opportunity to learn derivatives inside and out, forwards and backwards. Exciting, eh? Learning integration by substitution is almost as exciting as winning Deal or No Deal. Given a derivative that was produced by the chain rule, integration by substitution lets us work backwards to find an antiderivative. This method is also called ** u-substitution** because we usually use

*u*instead of some other letter.

We've done some integration by substitution already. We call it thinking backwards.

We can do integration by substitution using either Lagrange notation (primes *u'*) or Leibniz notation (fractions like ). While your teacher might have a preference, we don't care which of these ways you use. Just be careful not to mix them up. You can use primes (*u*') or you can use fractions , but don't use both in the same problem.