# Integration techniques

Contents

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.

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).

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

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

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

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.