In this tutorial, we will discuss the use of substitution when doing integration.
Substitution can be viewed as the reverse of the Chain Rule for derivatives.
Find the anti-derivative of the following functions using substitution
now we need to make our choice for 'u', as a general rule 'u' is usually the more complicated function (although this is not a good rule of thumb to always go by). The true reason we choose
This will simplify the integral to
pluggin 'u' back in and we get
Now let us choose u, in this case there is not really 'a more complicated function' as in the last example. We have to be a little clever, and choose the function such that when we take 'u' and the derivative of 'u' it will simplify the integral. An appropriate choice would be
this will simplify the integral to