U Substitution
What U substitution is is basically taking a complex function that you need to take the integral of and substitute U in it's place. Then you take the derivative of it and then substitute for the different variables. And then take the integrals of the u's and du's
Example Problem
Let's say you have the problem:
The first thing you need to do is to find what u is. From looking at this, we can tell that the u is most definitely 4x^3 + 5, since it's derivative is 12x^2 .
Then you substitute the U's in the equation.
Then you solve. The integral get's rid of the du and then you are left with the u which if you take the integral (see integral rules) you get:
You get the + c if it's an indefinite integral.
Now you substitute back in what equaled u.
Now you substitute back in what equaled u.
This equation could be simplified more but this is the basic premise of the concept.