# indefinite integral

• Dec 10th 2005, 07:28 AM
bobby77
indefinite integral
• Dec 10th 2005, 08:05 AM
CaptainBlack
Quote:

Originally Posted by bobby77

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Evaluate the indfinite integral:

$\displaystyle \int \frac{x^2-2x-3}{x-1}\ dx$

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Reduce the integrand to the sum of a linear term in x plus a constant
divided by another linear term in x. This can be done either by inspection
or synthetic division.

Then the integral should be elementary

RonL
• Dec 10th 2005, 08:35 AM
Jameson
Right. So basically this will reduce down to something easily integratable. But you have to be careful that once you integrate the reduced function to indicate the point of discontinuity. I would start by factoring.
• Dec 10th 2005, 11:27 AM
CaptainBlack
Quote:

Originally Posted by Jameson
Right. So basically this will reduce down to something easily integratable. But you have to be careful that once you integrate the reduced function to indicate the point of discontinuity. I would start by factoring.

The reduction process does not alter the position or nature
of the singularity, in fact it makes it more obvious if anything.

Also the position of the singularity is quite evident from
the form of the integral.

The nature of the singularity is that of: $\displaystyle 1/x$ which has a
singularity at $\displaystyle 0$, as does $\displaystyle ln(|x|)+c$, which is its indefinite integral.

That you have to be careful when using this to construct a definite integral
is something that has to be done for all integrals with singularities in the
range of integration.

(Also the use of the word elementary was slightly tongue in
cheek - meaning has an indefinite integral expressible in terms
of elementary functions)

RonL
• Dec 10th 2005, 11:42 AM
Jameson
Agreed. I was just making sure the poster realized that if he/she integrate the function over x=-1 to understand the problem.