Evaluate int_(11)^(e^(2)+10)(4x-41)/(x-10)dx. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).

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Evaluate  int_(11)^(e^(2)+10)(4x-41)/(x-10)dx. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).

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Simplify Integrand: Simplify the integrand if possible. The integrand (4x-41)/(x-10) can be simplified by long division since the degree of the numerator is equal to the degree of the denominator. We divide 4x by x to get 4 and multiply (x-10) by 4 to get 4x-40. We subtract this from the numerator to get a remainder of -1. So, the integrand simplifies to 4 - 1/(x-10).Split Integral: Split the integral into two simpler integrals. We can write the integral as the sum of two simpler integrals: ∫(4x-41)/(x-10) dx = ∫4 dx - ∫1/(x-10) dx.Integrate Terms: Integrate each term separately. The integral of 4 with respect to x is 4x, and the integral of 1/(x-10) with respect to x is ln|x-10|. So we have: ∫4 dx = 4x and ∫1/(x-10) dx = ln|x-10|.Combine Results: Combine the results and apply the limits of integration. Combining the results from the previous step, we get: ∫(4x-41)/(x-10) dx = 4x - ln|x-10| from 11 to e^(2)+10. Now we need to evaluate this expression from 11 to e^(2)+10: [4x - ln|x-10|] evaluated from 11 to e^(2)+10 = [4(e^(2)+10) - ln|e^(2)+10-10|] - [4(11) - ln|11-10|].Perform Evaluation: Perform the evaluation at the upper and lower limits. First, we evaluate at the upper limit e^(2)+10: 4(e^(2)+10) - ln|e^(2)+10-10| = 4e^(2) + 40 - ln|e^(2)|. Since e^(2) is positive, we can remove the absolute value: 4e^(2) + 40 - ln(e^(2)) = 4e^(2) + 40 - 2. Next, we evaluate at the lower limit 11: 4(11) - ln|11-10| = 44 - ln|1| = 44 - 0 (since ln(1) = 0).Subtract Limits: Subtract the lower limit evaluation from the upper limit evaluation. Now we subtract the lower limit result from the upper limit result: [4e^(2) + 40 - 2] - [44] = 4e^(2) + 40 - 2 - 44 = 4e^(2) - 6.Write Final Answer: Write the final answer. The final answer is the result of the subtraction from the previous step: 4e^(2) - 6.

Evaluate $\int_{11}^{e^{2}+10} \frac{4 x-41}{x-10} d x$ . Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).

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Evaluate ∫11e2+104x−41x−10dx \int_{11}^{e^{2}+10} \frac{4 x-41}{x-10} d x ∫11e2+10​x−104x−41​dx. Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).

Evaluate $\int_{11}^{e^{2}+10} \frac{4 x-41}{x-10} d x$ . Write your answer in simplest form with all logs condensed into a single logarithm (if necessary).