Antiderivative
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Antidifferentiation (or indefinite integration) is a part of mathematics, which is the opposite of differentiation. It is called indefinite integration because an equation is integrated without limits, so the result is an equation.
It is written as
- with the integral sign that has no limits
- the equation you are integrating
- and the which means "with respect to ", which does not mean anything with simple integration.
Finding a simple antiderivative
To find the antiderivative of a simple equation
- the power should be increased by 1
- the whole equation should be divided by the new power
- and a constant should be added (unlike definite integration).
This can be shown as:
The antiderivative of an equation with several power terms can also be found in the same way, by finding the antiderivative of each section on its own, and then adding or subtracting.
Examples
Changing fractions and roots into powers makes it easier: