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# Indefinite Integrals

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# Legrange (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 derivatives.

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.