Groups > comp.soft-sys.math.mathematica > #2649

Simple integral

From	Mariano Pierantozzi <mariano.pierantozzi@gmail.com>
Newsgroups	comp.soft-sys.math.mathematica
Subject	Simple integral
Date	2011-05-23 10:29 +0000
Organization	Steven M. Christensen and Associates, Inc and MathTensor, Inc.
Message-ID	<irdctv$3tq$1@smc.vnet.net> (permalink)

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Hi,
I've got some problem studing this simple integral:
Integrate[1/(x^2 + b x + c), x].
The Mathematica solution is:
(2 ArcTan[(b + 2 x)/Sqrt[-b^2 + 4 c]])/Sqrt[-b^2 + 4 c]

The problem is that my secon order polinomial have two real solutions, so my
delta (-b^2 + 4 c) is greater than zero. In this case the denominator of the
solution does not exist or exist in complex field, but my x is a volume...
I try in this way
Integrate[1/(x^2 + b x + c), x, Assumptions -> {-b^2 + 4 c < 0}], but
nothing!
I can't trasform my arcotangent in two log.
In summary I would like to have such a solution:
Integrate[1/(x^2 + 5 x + 6), x]
Log[2 + x] - Log[3 + x]
but in general form.
Sorry for my english!
Mariano Pierantozzi
PhD Student
Energy Engineering

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Simple integral Mariano Pierantozzi <mariano.pierantozzi@gmail.com> - 2011-05-23 10:29 +0000
  Re: Simple integral "p.ramsden" <p.ramsden@imperial.ac.uk> - 2011-05-23 12:41 +0000
  Re: Simple integral Stefan Salanski <wutchamacallit27@gmail.com> - 2011-05-24 09:59 +0000

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