68. Let n be a positive integer. Show that omuzA (d) othe far (In x)"dx = x(ln x)" – n (In x)"- dx. | The formula given in Exercise 67 reduces the calculation of Sx" ex dx to the calculation of ſ x"-leax dx. The formula given in Exercise 68 reduces the calculation of ((In x)" dx to the calculation of [ (ln x)"-l dx. Formulas (such as these) which reduce the calculation of an expression inn to the calculation of the corresponding expression in n – 1 are called reduction formulas. O
68. Let n be a positive integer. Show that omuzA (d) othe far (In x)"dx = x(ln x)" – n (In x)"- dx. | The formula given in Exercise 67 reduces the calculation of Sx" ex dx to the calculation of ſ x"-leax dx. The formula given in Exercise 68 reduces the calculation of ((In x)" dx to the calculation of [ (ln x)"-l dx. Formulas (such as these) which reduce the calculation of an expression inn to the calculation of the corresponding expression in n – 1 are called reduction formulas. O
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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