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

Answer 1

Isabella Ackerman

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Answer 2

Charles Anctil

To integrate ( \int \frac{x}{(x^2 - 1)(x - 1)} ) using partial fractions, you first factor the denominator into irreducible factors, which gives ( (x + 1)(x - 1)^2 ). Then, you express the fraction as the sum of partial fractions, where each denominator is one of the factors. After finding the appropriate constants, you integrate each term 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.