## 6.1 Antiderivatives of Functions

#### Antiderivatives of Specific Functions

- We will be looking at antiderivatives of polynomial, exponential and trigonometric functions.
- The formulas are as below:

##### i) Polynomial functions

\int x^{n} d x=\frac{1}{n+1} x^{n+1}+c \quad,\ n \neq-1

\int x^{-1} d x=\int \frac{1}{x} d x=\ln |x|+c

Note: Notice that in there is an absolute value over to make the result fit the domain for all logarithmic functions is (0,\ +\infty), and x=0 is not possible in the first place as it would make \frac{1}{x} undefined.