U Substitution can be used in specific cases. It is derived from the chain rule. Whenever an Integral contains a function and it's derivative, U Substitution is a candidate. Whenever the correct U has been chosen, the problem will be come easier because there will be some cancellation that can be made in the problem. After the cancellation is made, the original problem is translated into a basic integral that can easily be evaluated.
This video series covers how to select your U, and various examples of U substitution.
Examples covered in this series
1. Integral [ (x + 5)^3 dx ]
2. Integral [ (X+8)^5 dx ]
3. Integral [ cos(3x) dx ]
4. Integral [ (x^2 + 5)^2 * (2x) dx ]
4b. Integral [ (x^3 + 4)^5 * (x^2) dx ]
5. Integral [ 2x / (x^2 + 7) dx ]
6. Definite Integral [ e^(2x) dx ] 0 to 5
7. Definite Integral [ 2xe^(x^2) dx ] 0 to 3
8. Integral [ sin(2x) cos(2x) dx ]
9. Integral [ sin(3x) / cos(3x) dx ]
10. Integral [ tan(3x) dx ]
11. Integral [ sec^2 (x) * tan (x) dx ]
12. Integral [ 8/ sqrt(2x - 1) dx ]