022 Exam 2 Sample A, Problem 4

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Find the antiderivative of

This problem requires three 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 our power rule for integration:
  for .


Step 1:  
Use a u-substitution with This means , or . After substitution we have
Step 2:  
We can no apply the power rule for integration:
Step 3:  
Since our original function is a function of , we must substitute back into the result from step 2:
Step 4:  
As will all indefinite integrals, don't forget the constant  at the end.
Final Answer:  

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