Science:Math Exam Resources/Courses/MATH101/April 2008/Question 01 (f)
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Question 01 (f) 

Find the first three nonzero terms in the powerseries representation in powers of (i.e. the Maclaurin series) for 
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Hint 

What is the Maclaurin series expansion of
This should look very familiar to the problem at hand. 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Recall the following Maclaurin series expansion Now plugging in gives and then multiplying by gives Hence, the first three nonzero terms are Therefore, produces the first three nonzero terms of the desired integral. 