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### Integration by substitution

This method can be thought of as the reverse of the chain rule. To find , we first substitute . We differentiate this to obtain . Next, we change the limits, so the integral becomes . If the appropriate substitution was made, it should be possible to evaluate this integral directly. In the case of indefinite integration, we do the same and then substitute back for in the result.

This method can be used to find, for example, . We first substitute so that . Changing the limits, and substituting into the original integral gives .

Alexander Frolkin 2001-03-13