Evaluate int_(3)^(4)(2x^(2)-15 x+22)/(x-5)dx. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary). Submit Answer

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Evaluate  int_(3)^(4)(2x^(2)-15 x+22)/(x-5)dx. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary). Submit Answer

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Identify Integral: Identify the integral to be evaluated. We need to evaluate the integral of the function (2x^2 - 15x + 22)/(x - 5) from x = 3 to x = 4.Perform Long Division: Perform polynomial long division. Before integrating, we should simplify the integrand by performing polynomial long division of (2x^2 - 15x + 22) by (x - 5).Carry Out Division: Carry out the long division. Dividing 2x^2 by x gives 2x. Multiply (x - 5) by 2x to get 2x^2 - 10x. Subtract this from the original polynomial to get -5x + 22. Dividing -5x by x gives -5. Multiply (x - 5) by -5 to get -5x + 25. Subtract this from -5x + 22 to get -3. The result of the division is 2x - 5 with a remainder of -3. So, (2x^2 - 15x + 22)/(x - 5) = 2x - 5 - 3/(x - 5).Set Up Integral: Set up the integral with the simplified integrand. Now we can write the integral as: ∫(2x - 5) dx - ∫(3/(x - 5)) dx from x = 3 to x = 4.Integrate First Part: Integrate the first part of the simplified integrand. The integral of 2x - 5 with respect to x is x^2 - 5x.Integrate Second Part: Integrate the second part of the simplified integrand. The integral of 3/(x - 5) with respect to x is 3ln|x - 5|.Combine and Evaluate: Combine the integrals and evaluate from 3 to 4. The combined integral is (x^2 - 5x) - 3ln|x - 5| from x = 3 to x = 4.Evaluate Definite Integral: Evaluate the definite integral. Plug in the upper limit x = 4 and the lower limit x = 3 into the antiderivative and subtract the two results. For x = 4: (4^2 - 5*4) - 3ln|4 - 5| = (16 - 20) - 3ln|-1| = -4 - 3ln(1) For x = 3: (3^2 - 5*3) - 3ln|3 - 5| = (9 - 15) - 3ln|-2| = -6 - 3ln(2) Now subtract the lower limit result from the upper limit result: (-4 - 3ln(1)) - (-6 - 3ln(2)) = -4 + 6 - 3ln(1) + 3ln(2) = 2 + 3ln(2)Simplify Final Expression: Simplify the final expression. Since ln(1) is 0, the expression simplifies to 2 + 3ln(2).

Evaluate $\int_{3}^{4} \frac{2 x^{2}-15 x+22}{x-5} d x$ . Write your answer in simplest form with all logs condensed into a single logarithm (if necessary). $\newline$ Submit Answer

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Evaluate $\int_{3}^{4} \frac{2 x^{2}-15 x+22}{x-5} d x$ . Write your answer in simplest form with all logs condensed into a single logarithm (if necessary). $\newline$ Submit Answer