Science:Math Exam Resources/Courses/MATH105/April 2012/Question 03 (b)
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Question 03 (b) 

Evaluate the following definite integral: 
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 

Use partial fractions. As a first step you need to factor the denominator. 
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. One way to evaluate is to use partial fractions. We note that , and so we decompose the fraction into:
after multiplying through by the common denominator of . If we expand the equation out and find the coefficients of the respective powers of x then:
This tells us that and therefore . The integral is easy to evaluate now: We used the fact that above. 