022 Exam 2 Sample A, Problem 3
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Find the antiderivative of
Foundations:  

This problem requires two rules of integration. In particular, you need  
Integration by substitution (U  sub): If and are differentiable functions, then  
The Product Rule: If and are differentiable functions, then  
The Quotient Rule: If and are differentiable functions and , then  
Additionally, we will need our power rule for differentiation:  
 
as well as the derivative of natural log:  

Solution:
Step 1: 

Use a Usubstitution with This means , and after substitution we have

Step 2: 

We can now take the integral remembering the special rule: 
Step 3: 

Since this integral is an indefinite integral we have to remember to add C at the end. 
Final Answer: 
