Homework Help is Here – Start Your Trial Now!
Math
Calculus
(d) For n = 3, set f(x) = (In(x))³ and g'(x) = 1, using the "integration by parts" formula above, show that we have the relationship F3(x) = x(ln(x))³ – 3F2(x), and using (c), show that an antiderivative of (In(x))³ is F3(x) = x((In(x))³ – 3(ln(æ))² +6 ln(x) – 6). (e) Use the same idea as in (d), show that an antiderivative of (In(x))4 is FA(2) = x((In(x))* – 4(ln(x))³ +12(In(x))² – 24 In(x) + 24)

(d) For n = 3, set f(x) = (In(x))³ and g'(x) = 1, using the "integration by parts" formula above, show that we have the relationship F3(x) = x(ln(x))³ – 3F2(x), and using (c), show that an antiderivative of (In(x))³ is F3(x) = x((In(x))³ – 3(ln(æ))² +6 ln(x) – 6). (e) Use the same idea as in (d), show that an antiderivative of (In(x))4 is FA(2) = x((In(x))* – 4(ln(x))³ +12(In(x))² – 24 In(x) + 24)

Calculus: Early Transcendentals
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...
See similar textbooks
icon
Related questions
Question

In lectures we have an antiderivative of ln(x) is xln(x) - x. Here we like a formula for the antiderivative

Fn(x) = (ln(x))ndx

where n is a positive whole number.

In lectures we have an antiderivative of In(x) is x ln(x) – x. Here we like a formula for the antiderivative F„(x) = | (In(a))"dæ where n is a positive whole number.
Transcribed Image Text:In lectures we have an antiderivative of In(x) is x ln(x) – x. Here we like a formula for the antiderivative F„(x) = | (In(a))"dæ where n is a positive whole number.
(d) For n = 3, set f(x) = (In(æ))³ and g'(x) = 1, using the "integration by parts" formula above, show that we have the relationship F3(x) = x(ln(x))³ – 3F2(x), and using (c), show that an antiderivative of (In(x))³ is F3(x) = x((In(x))³ – 3(In(x))² + 6 ln(x) – 6). (e) Use the same idea as in (d), show that an antiderivative of (In(x))4 is F4(x) = x((In(x))4 – 4(ln(x))³ + 12(ln(x))² – 24 1n(x) + 24)
Transcribed Image Text:(d) For n = 3, set f(x) = (In(æ))³ and g'(x) = 1, using the "integration by parts" formula above, show that we have the relationship F3(x) = x(ln(x))³ – 3F2(x), and using (c), show that an antiderivative of (In(x))³ is F3(x) = x((In(x))³ – 3(In(x))² + 6 ln(x) – 6). (e) Use the same idea as in (d), show that an antiderivative of (In(x))4 is F4(x) = x((In(x))4 – 4(ln(x))³ + 12(ln(x))² – 24 1n(x) + 24)
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS