Integrate by Parts → Product Rule

It's the Reverse Product Rule. And here is the formula to solve the integration by parts:

image

Refer to Khan academy: Integration by parts intro

Trick & Strategy:

  • Recognize it's an integral with functions' product:

  • Carefully choose which function to be f(x) and the other to be g'(x).

  • Better to choose the easier one as f(x) when taking derivative.

Example

image Solve: [Refer to Symbolab](https://www.symbolab.com/solver/step-by-step/\int_{0}^{\pi} x\cdot sin\left(2x\right)dx)

Example

image Solve: image

Last updated