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Integrate: 14 9x²+2x-1 (x-1)(2x²+7x-4) dx

Integrate: 14 9x²+2x-1 (x-1)(2x²+7x-4) dx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve it by Partial Fraction

**Integrate:** \[ \int_{2}^{14} \frac{9x^2 + 2x - 1}{(x-1)(2x^2 + 7x - 4)} \, dx \] This integral involves a rational function, where the numerator is a polynomial \(9x^2 + 2x - 1\) and the denominator is a product of polynomials \((x-1)(2x^2 + 7x - 4)\). The definite integral is evaluated from \(x = 2\) to \(x = 14\). This type of problem typically requires partial fraction decomposition to simplify the integrand before integrating.
Transcribed Image Text:**Integrate:** \[ \int_{2}^{14} \frac{9x^2 + 2x - 1}{(x-1)(2x^2 + 7x - 4)} \, dx \] This integral involves a rational function, where the numerator is a polynomial \(9x^2 + 2x - 1\) and the denominator is a product of polynomials \((x-1)(2x^2 + 7x - 4)\). The definite integral is evaluated from \(x = 2\) to \(x = 14\). This type of problem typically requires partial fraction decomposition to simplify the integrand before integrating.
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