Remember the chain rule? This is how we undo that. Use this whenever you want to integrate a function that has an inside function.
- Assign the variable ‘u’ to the inside function. It helps if the derivative of ‘u’ also appears in the function.
- Take the derivative u, and isolate du.
- If necessary, manipulate constants.
- Substitute- write integral in terms of ‘u’.
- Integrate.
To use u-substitution, you follow the same rules as we use for indefinite integrals. However, you have to put your limits in terms of u, do NOT put your expression in terms of x after you plug in u, and of course use the Fundamental Theorem. If you do not want to change your limits, you can put everything back in terms of x after you integrate, and keep your limits in terms of x.