Explanation Given Information: The provided integral is ∫ 5 7 x 2 − 25 d x Formula used: For any variable u , the integral formula is, ∫ u 2 − a 2 d u = 1 2 ( u u 2 − a 2 − a 2 ln | u + u 2 − a 2 | ) + C Where, ‘ a’ is not a function of u . and C is the constant of integration . Calculation: Consider the provided integral, ∫ 5 7 x 2 − 25 d x The integral can be rewritten as: ∫ 5 7 x 2 − 5 2 d x The integral is similar to the integral formula, ∫ u 2 − a 2 d u . Therefore, the formula used is ∫ u 2 − a 2 d u = 1 2 ( u u 2 − a 2 − a 2 ln | u + u 2 − a 2 | ) + C . Now, use the formula ∫ u 2 − a 2 d u = 1 2 ( u u 2 − a 2 − a 2 ln | u + u 2 − a 2 | ) + C and compare from the provided integral ∫ 5 7 x 2 − 25 d x

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ISBN: 9780357865095

Author: HARSHBARGER

Publisher: CENGAGE L

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Chapter 13.5, Problem 11E

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To calculate: The value of the integral ∫57x2−25dx.

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The value of the integral ∫ 5 7 x 2 − 25 d x .

Solution Summary: The author explains how to calculate the value of the provided integral, displaystyleint_57sqrt

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To calculate: The value of the integral ∫57x2−25dx.

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Chapter 13 Solutions