Science:Math Exam Resources/Courses/MATH105/April 2016/Question 02 (c)
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Question 02 (c) 

Evaluate . 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Factorize the denominator and use the partial factions method. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since the degree of the numerator is smaller than the denominator which is 3 here, we use partial fractions to evaluate the integral. The denominator is , so we split the denominator as the following,
We find the numerator by computing the common denominator
We simplify the numerator and make it equal to to get
Matching the coefficient, we find the following equations for : which gives:
