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

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

Example

Solve: