Definite Integration of Power Functions

$$\displaystyle \int_{n}^{m}{(ax+b)^n}dx = \dfrac{1}{a(n+1)}\big[(ax+b)^{n+1}\big]_{n}^{m}+c$$

Example 1

Find $\displaystyle \int_{0}^{1}{(2x+1)^5}dx$.

Example 2

Find $\displaystyle \int_{0}^{1}{\dfrac{1}{(3x-2)^4}}dx$.

Example 3

Find $\displaystyle \int_{0}^{1}{\sqrt{4x+3}}dx$.