### Quick description

This article describes a number of methods for working out integrals of the form , where and are variables rather than constants. This amounts to finding a function that differentiates to , in which case (by the fundamental theorem of calculus).

When written, it should contain accounts of integration by parts and substitution, and also the trick of just spotting that the integrand has the form (in which case you find a function that differentiates to and your answer is ). Another trick is guessing a function and then adjusting it afterwards. (For example, to integrate , you could guess , since that will at least give you a term in the answer, and then subtracts to get rid of the extra that you don't want.) Most of the article should be understandable by bright high-school students.

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