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How do you integrate #int (3x^2-15x+23)/((2x+1)(x-2)^2)# using partial fractions?

Answer 1

Paisley Johnson

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Answer 2

Isaiah Allen

User prefers answers without irrelevant information or introduction words.To integrate (\int \frac{3x^2 - 15x + 23}{(2x + 1)(x - 2)^2} ) using partial fractions, you first express the integrand as a sum of simpler fractions:

(\frac{3x^2 - 15x + 23}{(2x + 1)(x - 2)^2} = \frac{A}{2x + 1} + \frac{B}{x - 2} + \frac{C}{(x - 2)^2})

Multiplying both sides by ((2x + 1)(x - 2)^2) to clear the denominators gives:

(3x^2 - 15x + 23 = A(x - 2)^2 + B(2x + 1)(x - 2) + C(2x + 1))

Expanding and matching coefficients, you find the values of A, B, and C. Then, 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.