Simple integral
- To: mathgroup at smc.vnet.net
- Subject: [mg119174] Simple integral
- From: Mariano Pierantozzi <mariano.pierantozzi at gmail.com>
- Date: Mon, 23 May 2011 06:29:28 -0400 (EDT)
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