Antidifferentiation Formulas

In this topic:

    (1) State some basic antidifferentiation formulas.
    
    (2) Find the most general antiderivative of the function
    
    (3) Find the most general antiderivative of the function
    
    (4) Find given
    

Here are some basic antidifferentiation formulas followed by some examples on how to use them.

Constant Multiple:    

Sum Rule:         

Difference Rule:     

Linearity Rule:     

Constant Rule:     

Exponential Rule:     

Power Rule:         

Trigonometric Rules:













Inverse Trigonometric Rules:

Example (Antiderivative Formulas) Find the most general antiderivative of the function

    Solution. We want to evaluate Since, we find,
    

Example (Antiderivative Formulas) Find the most general antiderivative of the function

    Solution. We want to evaluate Since,



we use the linearity rule and the power rule to find,
    

Example (Antiderivative Formulas) Find given

    Solution. First we find by,
    


where is some constant which can be determined given So,



So in fact, Now to find we follow the same procedure,




where is a constant which can be determined given So,



Therefore, as desired.

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Antidifferentiation Formulas
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/antidifferentiation-formulas.html