022 Exam 2 Sample B, Problem 5

From Math Wiki
Revision as of 12:01, 18 May 2015 by MathAdmin (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search

Find the antiderivative of

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:


Step 1:  
Use a u-substitution with This means . 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