Integration of Power Functions

$$\displaystyle \int{(ax+b)^n}dx = \dfrac{(ax+b)^{n+1}}{a(n+1)}+c$$

Example 1

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

Example 2

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

Example 3

Find $\displaystyle \int{\sqrt{4x+3}}dx$. Note: This formula works only for the power of linear functions, such as $\displaystyle \int{(2x+6)^7}dx, \int{(1-3x)^6}dx$,
but does not apply for non-linear expressions such as $\displaystyle \int{(x^2+3)^4}dx, \int{(x^3+x^2+2)^6}dx$.