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- Dec 10th 2005, 07:28 AMbobby77indefinite integral
please see the attatchment...

- Dec 10th 2005, 08:05 AMCaptainBlackQuote:

Originally Posted by**bobby77**

Which asks:

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 AMJameson
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 AMCaptainBlackQuote:

Originally Posted by**Jameson**

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 AMJameson
Agreed. I was just making sure the poster realized that if he/she integrate the function over x=-1 to understand the problem.