Students will learn how to derive recurrence relations for integrals. Students will learn how integration by parts can be used to find recurrence relations for each of the following:

$$\begin{align} & \int \sin^n x dx \\ & \int x^ne^x dx \end{align}$$Then students will learn how one of the Pythagorean identities can be used to find a recurrence relation for

$$\int \tan^n x dx$$For a fantastic lesson, watch this, then this, and finally, this.

Conclude by giving your students these challenges:

- U in a Pentagon by NRICH
- Vectors Round a Square by NRICH
- Holly by NRICH
- Matchless by NRICH