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How do you integrate #int (5x^2-6x+13) / [(x^2+x+1)(x-2)]# using partial fractions?

Answer 1

Ezra Adams

See the answer below:

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Answer 2

Emilia Aguilar

To integrate ( \frac{5x^2 - 6x + 13}{(x^2 + x + 1)(x - 2)} ) using partial fractions, follow these steps:

Factor the denominator ( (x^2 + x + 1)(x - 2) ).
Express ( \frac{5x^2 - 6x + 13}{(x^2 + x + 1)(x - 2)} ) as the sum of partial fractions, each with a simpler denominator.
Find the unknown constants by equating the numerators of the partial fractions to the original expression.
Integrate each partial fraction individually.
Combine the integrated partial fractions to get the final result.

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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.