# Integration techniques

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Some functions don't make it easy to find their integrals, but we are not ones to give up so fast! Learn some advanced tools for integrating the more troublesome functions.

## Integration by parts

Learn how to use the product rule in order to find the integral of a product of functions (sadly this is more complicated than using the product rule the regular way).

## Partial fraction expansion

Learn a useful algebraic tool to find the integrals of some rational functions.

## u-substitution

u-substitution is an extremely useful technique. Harnessing the power of the chain rule, it allows us to define a new variable (common denoted by the letter u) as a function of x, and obtain a new expression which is (hopefully) easier to integrate.

## Reverse chain rule

Reverse chain rule is another, faster way to think about u-substitution.

## Integration using trigonometric identities

Some integrals that contain trig functions demand that we manipulate those functions using trig identities in order to find the integral.

## Trigonometric substitution

Another super useful technique for computing integrals involves replacing variables with trigonometric functions. This can make things seem a little more complicated at first, but with the help of trigonometric identities, this technique makes certain integrals solvable.