Solving a simple integral

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Homework Statement


##\displaystyle \int \frac{1}{x^2+a} dx##

Homework Equations




The Attempt at a Solution


I know that I can convert this to the form ##\displaystyle \int \frac{1}{x^2+(\pm \sqrt{a})^2} dx## = ##\displaystyle \frac{1}{\pm \sqrt{a}} \arctan (\frac{x}{\pm \sqrt{a}}) + C##, but I don't know whether to take the positive or the negative root.
 

Answers and Replies

  • #2
Orodruin
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Ask yourself whether it matters or not.
 
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  • #3
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Ask yourself whether it matters or not.
Does it not matter since ##\arctan## is an odd function, so in either case you get ##\displaystyle \frac{1}{\sqrt{a}} \arctan (\frac{x}{\sqrt{a}}) + C##?
 
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Orodruin
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Indeed.
 
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