Science:Math Exam Resources/Courses/MATH103/April 2010/Question 01 (b)
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Question 01 (b) 

Multiple Choice Question: Exactly ONE of the answers provided is correct. There is no partial credit in this questions. To find the integral using integration by parts, the best choice for u and dv in the first step would be 
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Hint 

You can either try each case or try to guess what would happen if you tried each case without actually writing each. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We want to integrate with integration by parts. We have three possible products:
b) c)
The second product also doesn't make sense because the second term is not easy to integrate. Also choosing as and as is not good since integrating AND derivating makes the equation more complicated. So it must be the third product. It doesn't matter, if we choose as or because the integral is the same (excapt for constants). If we choose as , we get as , what makes the equation more complicated. So we take as and get and and get . That simplified the equation. So we take answer ii. Integration would work now like this: 