Question

integration by substitution​

Answer 1

Answer:

integration by substitute

Step-by-step explanation:

Integration by Substitution" (also called "u-Substitution" or "The Reverse Chain Rule") is a method to find an integral, but only when it can be set up in a special way.

The first and most vital step is to be able to write our integral in this form:

integration by substitution general

Note that we have g(x) and its derivative g'(x)

Like in this example:

integration by substitution cos(x^2) 2x dx

Here f=cos, and we have g=x2 and its derivative 2x

This integral is good to go!

When our integral is set up like that, we can do this substitution:

integration by substitution general

Then we can integrate f(u), and finish by putting g(x) back as u.