We have changed our privacy policy. In addition, we use cookies on our website for various purposes. By continuing on our website, you consent to our use of cookies. You can learn about our practices by reading our privacy policy.
© 2016 Shmoop University, Inc. All rights reserved.
Indefinite Integrals

Indefinite Integrals

Lagrange (Prime) Notation

When we use the chain rule to take derivatives, there are some patterns that show up a lot. Some examples are

We can use these patterns to find indefinite integrals.

The general strategy for integration by substitution has three steps:

  • Change variables (substitute in u for some function of x).
  • Apply an appropriate pattern to find the indefinite integral.
  • Put the original variable back (substitute the function of x back in for u).

The trickiest part is usually figuring out which function we want to replace with u. Here are two guidelines that might help:

  • u should be as complicated as possible, but still an "inside" function.
  • u' should be similar to something else already in the function.

People who Shmooped this also Shmooped...