Integration by parts is another very useful integration technique. U-Substitution or the simple power rule may not always be applicable, so integration by parts can be useful in some of those other problems. Examples are provided below.
Form: Integration by parts will always be solved like this: \[uv - ∫vdu\] LIPET method: Whatever term occurs first in LIPET becomes your "u" term, while the other term becomes your "dv" term".
Logarithm Inverse trig function Polynomial Exponential Trig function
Steps: 1. Use the LIPET rule to decide which term to make your "u" and what term to make your "dv" 2. Take the derivative of the "u" term, creating the "du" term. Take the integral of the "dv" term, creating the "v" term 3. Plug the terms into the form shown above 4. Repeat steps 1-3 if further integration is needed. I suggest to use different variables other than "u" and "v" to not get confused