Mathematics
Mathematics, 03.03.2020 18:25, KinG5152

(9x2 + 10x + 4) βˆ’ (9x2 + 5x βˆ’ 1)

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Answers: 3

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Evaluate 8x2 + 9x βˆ’ 1 2x3 + 3x2 βˆ’ 2x dx. solution since the degree of the numerator is less than the degree of the denominator, we don't need to divide. we factor the denominator as 2x3 + 3x2 βˆ’ 2x = x(2x2 + 3x βˆ’ 2) = x(2x βˆ’ 1)(x + 2). since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form† 8x2 + 9x βˆ’ 1 x(2x βˆ’ 1)(x + 2) = correct: your answer is correct. to determine the values of a, b, and c, we multiply both sides of this equation by the product of the denominators, x(2x βˆ’ 1)(x + 2), obtaining 8x2 + 9x βˆ’ 1 = a correct: your answer is correct. (x + 2) + bx(x + 2) + cx(2x βˆ’ 1).
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