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Antidifferentiation (also called indefinite integration) is a part of mathematics. It is the opposite of differentiation. Antidifferentiation is integration with no limits (which is why it is called indefinite). The answer to an antiderivative 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.

Simple integration[change | change source]

To integrate

  • Add 1 to the power , so is now
  • Divide all this by the new power, so it is now
  • Add constant , so it is now

This can be shown as:

When there are many terms, integrate each part on its own:

(This only works if the parts are being added or taken away.)

Examples[change | change source]

Changing fractions and roots into powers makes it easier:

Integrating a bracket ("chain rule")[change | change source]

If you want to integrate a bracket like , we need to do it a different way. It is called the chain rule. It is like simple integration. It only works if the in the bracket has a power of 1 (it is linear) like or (not or ).

To do

  • Add 1 to the power , so that it is now
  • Divide all this by the new power to get
  • Divide all this by the derivative of the bracket to get
  • Add constant to give

Examples[change | change source]

Related pages[change | change source]