# What is #int (x^3-2x^2+6x+9 ) / (-x^2- x +3 )#?

First, we must decide what we want to do. Whenever you see a rational function (i.e. a polynomial divided by a polynomial), you want to use partial fraction decomposition (PFD).

We're going to take out a negative sign from the denominator and bring it back after the integral. Therefore, we want to be able to integrate

The first step in PFD is always to have the upper degree (currently 3) be lower than the lower degree (2). Therefore, we can start long dividing our polynomials:

Therefore, we have taken the original and made it much more manageable (well at least when it uses a bunch of variables to make it clear)

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The result of ( \frac{{x^3 - 2x^2 + 6x + 9}}{{-x^2 - x + 3}} ) is ( x - 3 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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