Science:Math Exam Resources/Courses/MATH101/April 2012/Question 03 (a)
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Question 03 (a) 

Evaluate 
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 

A bad function in the integrand will look much better when it is differentiated. Is there an integration technique that involves a differentiation step? 
Hint 2 

Try integration by parts. 
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. The bad part of the integrand is . The hints says we'd like to differentiate it (to make it 1/x). The relevant integration technique that involves differentiation is then integration by parts. First we identify and , then, by antidifferentiation, and by diffentiation. It seems we are not getting an integral that is harder then before, so let's move on and apply integration by parts: 