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How do you integrate #int(x+1)/((x^2-7)(x-3))# using partial fractions?

Answer 1

Samantha Adkison

See answer below:

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Answer 2

Evelyn Agard

To integrate the expression (x+1)/((x^2-7)(x-3)) using partial fractions, you first factor the denominator. After factoring, you express the rational function as a sum of simpler fractions using partial fraction decomposition. In this case, the denominator factors as (x^2 - 7)(x - 3) = (x + √7)(x - √7)(x - 3). Then, you express the original expression as:

(x + 1)/((x^2-7)(x-3)) = A/(x + √7) + B/(x - √7) + C/(x - 3)

where A, B, and C are constants to be determined. To find these constants, you can multiply both sides by the denominator and then equate coefficients of like terms. After finding A, B, and C, you integrate each term separately. This approach allows you to integrate the original expression by integrating each simpler fraction separately.

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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.