# Indefinite Integral of Rational Functions

## Understanding Indefinite Integral of Rational Functions

Using Indefinite Integral of Rational Functions requires that the format of the expression must be power of linear expressions, such as $(3x-1)^3, (2x+3)^3, \sqrt{4x-1}$, etc. $(3x^2-1)^3, (2\sqrt{x}+3)^3, \sqrt{4x^3-1}$ are not applicable for this formula.
$$\displaystyle \int{(ax+b)^n}dx = \dfrac{(ax+b)^{n+1}}{a(n+1)} + C \ (n \ne -1)$$

# Practice Questions

### Question 1

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

### Question 2

Find $\displaystyle \int{\sqrt{3x+2}}dx$.

### Question 3

Find $\displaystyle \int{\frac{1}{(5x+4)^2}}dx$.

### Question 4

Find $\displaystyle \int{\frac{1}{\sqrt{6x-1}}}dx$.

### Question 5

Find $\displaystyle \int{\sqrt[3]{(2-3x)^4}}dx$.