Some integrals contain square roots. In these you can have two types of substitution. Make sure you know how to handle these types.

Example : Method 1

Example:

  1. \displaystyle\int {x\sqrt {3x - 1} {\text{ }}} dx {\hphantom{aaa} \text{let}\hphantom{aa}}u = 3x - 1

Example: Method 2

Example:

  1. \displaystyle\int {x\sqrt {3x - 1} {\text{ }}} dx {\hphantom{aaa} \text{let}\hphantom{aa}}{u^2} = 3x - 1