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Representing a function as a power series 
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#1
Apr2708, 09:49 PM

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1. The problem statement, all variables and given/known data
Evaluate the indefinite integral as a power series and find the radius of convergence [tex]\int\frac{xarctan(x)}{x^3}[/tex] I have no idea where to start here. Should I just integrate it first? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 


#2
Apr2708, 10:49 PM

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Sure, you could do that. But, I think what they want to do is expand arctan(x) as a power series around 0 and then integrate.



#3
Apr2808, 11:56 AM

P: 23

ok. So arctan(x) = [tex]\int\frac{1}{1+x^2}[/tex]
= [tex]\int\sum (x^(2*n))[/tex] = [tex]\sum\frac{x^(2(n+1)}{2(n+1)}[/tex] is this what you mean? 


#4
Apr2808, 01:41 PM

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Representing a function as a power series
That's one way to get a series for arctan, yes. But you forgot a (1)^n factor. The expansion of 1/(1x) has all plus signs. 1/(1+x) doesn't.



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