022 Exam 2 Sample A, Problem 3

From Math Wiki
Revision as of 07:45, 16 May 2015 by MathAdmin (talk | contribs)
Jump to navigation Jump to search

Find the antiderivative of


Foundations:  
This problem requires two rules of integration. In particular, you need
Integration by substitution (u - sub): If   is a differentiable functions whose range is in the domain of , then
We also need the derivative of the natural log since we will recover natural log from integration:

 Solution:

Step 1:  
Use a u-substitution with This means , or . After substitution we have
Step 2:  
We can now take the integral remembering the special rule:
Step 3:  
Now we need to substitute back into our original variables using our original substitution
to find 
Step 4:  
Since this integral is an indefinite integral, we have to remember to add a constant  at the end.
Final Answer:  

Return to Sample Exam