Science:Math Exam Resources/Courses/MATH103/April 2009/Question 04 (b)
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Question 04 (b) 

Find 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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

This is a typical question for integration by parts. Recall the formula What is the easiest choice for u and dv? Sometimes you have to do integration by parts twice to get to your final answer... 
Hint 2 

Use integration by parts with and . 
Hint 3 

Then use integration by parts a second time with and . 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. For calculating this integral we use integration by parts two times. We take and . Then and (don't forget the derivative 1/x of ln(x)). for a constant c. 