Science:Math Exam Resources/Courses/MATH101/April 2015/Question 04 (b)
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Question 04 (b) 

Calculate 
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 fraction decomposition. 
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. Using partial fraction decomposition, we can write the integrand as for some constants . We find that , which implies that The first integral on the righthand side of the equation can be easily evaluated: On the other hand, to compute the second integral, we can use the substitution . Then and , which gives Combining these, we obtain 