For integration by parts , are we allowed to use the tabular method or do we have to solve all integration by parts questions using the setup as shown in the video?
@@16mhz98 Tabular method works in general. You simply learn the three kinds of stops that you will have, and know how to solve them. Stop 1: you reduce the differentiation column to zero. Common for polynomial functions in the differentiation column. Stop 2, the looper: You would otherwise be in an infinite loop, but you can spot the original integral in your integration column, or across a row. As you construct the output, assign the variable I to the original integral on both sides of the equation. Solve for I to get your solution. This is common for a mixture of trig and exponential functions. Stop 3: you can integrate your final row by another method, not involving integration by parts. Such as regrouping algebraic terms to something you can integrate by substitution. This is common for a mixture of logs and algebraic functions, or inverse trig and algebraic functions.
Brook Taylor invented it. He's the same Taylor who is the namesake of the Taylor Series. Learn the tabular method, also called the DI method. It is so much easier and a lot easier to keep track of your work than using the original formula.