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.
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).
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.
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.
Reverse chain rule is another, faster way to think about u-substitution.
Learn a useful algebraic tool to find the integrals of some rational functions.
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