How do you integrate #(x^2 + 3x +1)/(x^2 - x - 6)#?

Answer 1

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Answer 2

To integrate the rational function (\frac{x^2 + 3x + 1}{x^2 - x - 6}), you can first perform polynomial long division to rewrite it as the sum of a polynomial and a proper rational function. Then, you can integrate each part separately. After dividing (x^2 + 3x + 1) by (x^2 - x - 6), you get (1 + \frac{7x + 7}{x^2 - x - 6}). The integral of the constant term 1 is simply (x), and for the proper rational function (\frac{7x + 7}{x^2 - x - 6}), you can decompose it into partial fractions. After decomposing, you can integrate each term separately using standard integration techniques such as substitution or partial fractions.

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Answer from HIX Tutor

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.

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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