6.1 Antiderivatives of Functions
Antiderivatives of Specific Functions
- We will be looking at antiderivatives of the 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.
ii) Exponential functions
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