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Integrating irreducible quadratic factors

How do you integrate

1/x^(2)+x+1

and 3/x^(2)-6x+13
Complete the square then make a substitution to get it in the form 1/(u^2 +- 1)
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Avatar for Phichi
Phichi
11
Have you done trig substitutions? Are you doing further maths?
Alternatively, you could factorise it in terms of its roots in C\mathbb{C}, then do partial fractions. The fact that it has no factors over Q\mathbb{Q} doesn't really matter - just makes it a little bit less easy to write the working out. (Completing the square is probably the nicer way, to be honest.)
Original post by Smaug123
Alternatively, you could factorise it in terms of its roots in C\mathbb{C}, then do partial fractions. The fact that it has no factors over Q\mathbb{Q} doesn't really matter - just makes it a little bit less easy to write the working out. (Completing the square is probably the nicer way, to be honest.)


Although this does sound like the method my teachers used to get very annoyed at me using :colondollar:
Original post by Principia
Although this does sound like the method my teachers used to get very annoyed at me using :colondollar:

I don't see why - it's kind of neat…
Original post by Smaug123
I don't see why - it's kind of neat…


I think they objected to me making things "unnecessarily complex"...
(edited 9 years ago)

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