Change of variables can be used when u substitution does not easily show the derivative of one term within the integral. It is similar to u substitution because the goal is to take a complicated integral and reduce it to something manageable by making the substitution. In the end you are very likely to get a polynomial in your answer.
One use is when you have the same variable appear twice in an integral with one possible inside of a square root.
This process is very tricky. It will be helpful to write down all the steps to take.
1. Integral[ x * sqrt(2x -1) dx]
2. Definite Integral[ x * sqrt(x -7) dx] from 2 to 8
3. Integral[ (2x + 1) / sqrt(x + 4) dx ]
4. Definite Integral [3x / sqrt(2x -1) dx ] from 1 to 5
5. Definite Integral [x^2 * sqrt(x + 2) dx] from 2 to 7