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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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Transcribed Image Text:68. Let n be a positive integer. Show that omuA (d)
o
the
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.
-
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