Science:Math Exam Resources/Courses/MATH101/April 2017/Question 08
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Question 08 

8. Evaluate . A calculatorready answer is sufficient. 
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 into monimials. Use partial fraction decomposition to split the integrand into simpler expressions with denominator one of factors (up to multiplicity). 
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. First note that the denominator of the integrand factorizes as Thus, we want to use partial fractions to decompose the fraction into the form
By multiplying through by the denominator of the left hand side and then equating coefficients, we get that . Thus we can rewrite our integral as
Integrating, we get Answer: 