Find the value of int_(3)^(5)(3dx)/(7-x). Express your answer as a constant times ln 2. Answer: ◻ln 2

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Find the value of  int_(3)^(5)(3dx)/(7-x). Express your answer as a constant times  ln 2. Answer:  ◻ln 2

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Recognize standard form: Recognize the integral as a standard form. The integral of the form ∫(A dx)/(B - x) can be solved by recognizing it as a natural logarithm function. The integral ∫(dx)/(a - x) is equal to -ln|a - x| + C, where C is the constant of integration.Adjust to match form: Adjust the integral to match the standard form. To match the standard form, we need to factor out the constant from the numerator. In this case, the constant is 3, so we can write the integral as 3 * ∫(dx)/(7 - x).Apply standard form: Apply the integral. Now we can integrate using the standard form: ∫(dx)/(7 - x) = -ln|7 - x| + C So, 3 * ∫(dx)/(7 - x) = 3 * (-ln|7 - x| + C)Evaluate definite integral: Evaluate the definite integral from 3 to 5. We need to evaluate the antiderivative at the upper and lower limits and subtract: 3 * [-ln|7 - x|] evaluated from 3 to 5 = 3 * [-ln|7 - 5| + ln|7 - 3|] = 3 * [-ln|2| + ln|4|]Simplify expression: Simplify the expression. Since ln|4| = ln(2^2) = 2ln|2|, we can simplify the expression: 3 * [-ln|2| + 2ln|2|] = 3 * [ln|2|] = 3ln|2|Express final answer: Express the answer as a constant times ln 2. The final answer is already in the form of a constant times ln 2, so we can write it as: 3ln|2|

Find the value of $\int_{3}^{5} \frac{3 d x}{7-x}$ . Express your answer as a constant times $\ln 2$ . $\newline$ Answer: $\square \ln 2$

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Find the value of ∫353dx7−x \int_{3}^{5} \frac{3 d x}{7-x} ∫35​7−x3dx​. Express your answer as a constant times ln⁡2 \ln 2 ln2.\newlineAnswer: □ln⁡2 \square \ln 2 □ln2

Find the value of $\int_{3}^{5} \frac{3 d x}{7-x}$ . Express your answer as a constant times $\ln 2$ . $\newline$ Answer: $\square \ln 2$