Evaluate int_(3)^(9)(2x^(2)-13 x+15)/(x-2)dx. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).

Question

Evaluate  int_(3)^(9)(2x^(2)-13 x+15)/(x-2)dx. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).

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Perform Polynomial Long Division: Perform polynomial long division to simplify the integrand. We need to divide the polynomial 2x^2 - 13x + 15 by x - 2.Split Integrals: Split the integral into two separate integrals. ∫(2x - 3 + 9/(x - 2))dx = ∫(2x - 3)dx + ∫(9/(x - 2))dxIntegrate Terms Separately: Integrate each term separately. The integral of (2x - 3) is x^2 - 3x, and the integral of 9/(x - 2) is 9ln|x - 2|. ∫(2x - 3)dx = x^2 - 3x ∫(9/(x - 2))dx = 9ln|x - 2|Combine Integrals: Combine the integrals and evaluate from 3 to 9. The combined integral is (x^2 - 3x + 9ln|x - 2|) from 3 to 9.Evaluate Definite Integral: Evaluate the definite integral. Plug in the upper limit (9) and the lower limit (3) into the antiderivative and subtract. F(9) = 9^2 - 3*9 + 9ln|9 - 2| F(3) = 3^2 - 3*3 + 9ln|3 - 2|Perform Calculations for Limits: Perform the calculations for each limit. F(9) = 81 - 27 + 9ln(7) F(3) = 9 - 9 + 9ln(1)Subtract Limits: Subtract F(3) from F(9) to get the final result. F(9) - F(3) = (81 - 27 + 9ln(7)) - (9 - 9 + 9ln(1))Simplify Expression: Simplify the expression. F(9) - F(3) = 81 - 27 + 9ln(7) - 9 + 9 + 0 F(9) - F(3) = 54 + 9ln(7)

Evaluate $\int_{3}^{9} \frac{2 x^{2}-13 x+15}{x-2} d x$ . Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).

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Evaluate ∫392x2−13x+15x−2dx \int_{3}^{9} \frac{2 x^{2}-13 x+15}{x-2} d x ∫39​x−22x2−13x+15​dx. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).

Evaluate $\int_{3}^{9} \frac{2 x^{2}-13 x+15}{x-2} d x$ . Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).