Science:Math Exam Resources/Courses/MATH101/April 2007/Question 03 (b)
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Question 03 (b) 

FullSolution Problem. Justify your answers and show all your work. Simplification of answers is not required. Evaluate the following 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 

Try partial fractions. 
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. We proceed by partial fractions. First, we solve for the constants in
As the denominators above are equal, the numerators must also be equal and so
Now, plugging in into the above gives
and simplifying gives . Plugging in into the above yields
and so . Therefore, we have
completing the question. 