MAT136H1 Lecture Notes - Antiderivative

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4 Feb 2013
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5.5 Integration & Anti-derivatives
Method of Substitution
Question #1 (Easy): Evaluating the Indefinite Integral
Strategy
Sometimes the Chain Rule taking place in the integral is obvious. Usually they are grouped together
within distinct type of functions, such as trigonometric, exponential, square roots, etc.
Indefinite integral represents the entire family of all possible anti-derivate functions. Thus, the constant
factor must be added.
Sample Question
Evaluate the indefinite integral using the method of substitution.
      
Solution
Let     , then       .
This fits the given expression straightaway. Thus, using the method of substitution the indefinite integral
can be written as:        


  
 
Substituting back in the original variable :
 
    
 
Therefore, the indefinite integral is evaluated as:       
    
 .
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