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Use integration by parts to establish the reduction formula. n ах хе ax dx = n-1 е ахxdx, a #0 a ..... First, select appropriate values for u and dv. u = and dv = dx Now, find du and v. Treat a and n as constants. du = dx and v = Now, make substitutions in the integration by parts formula and simplify. ax dx = dx Finally, apply the constant multiple rule to complete the proof. n ax хе ax dx = dx a x-1eax — 1.ах n - x"-'eax a ах e a n- 1 nx" -'eax

Use integration by parts to establish the reduction formula. n ах хе ax dx = n-1 е ахxdx, a #0 a ..... First, select appropriate values for u and dv. u = and dv = dx Now, find du and v. Treat a and n as constants. du = dx and v = Now, make substitutions in the integration by parts formula and simplify. ax dx = dx Finally, apply the constant multiple rule to complete the proof. n ax хе ax dx = dx a x-1eax — 1.ах n - x"-'eax a ах e a n- 1 nx" -'eax

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...
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Use integration by parts to establish the reduction formula. n ах хе ax dx = n-1 е ахxdx, a #0 a ..... First, select appropriate values for u and dv. u = and dv = dx Now, find du and v. Treat a and n as constants. du = dx and v = Now, make substitutions in the integration by parts formula and simplify. x" e ax dx = (D - |O dx Finally, apply the constant multiple rule to complete the proof. n ax хе ax dx = dx a xn-1eax n - x"-'eax a ах e a n- 1 nx" -'eax
Transcribed Image Text:Use integration by parts to establish the reduction formula. n ах хе ax dx = n-1 е ахxdx, a #0 a ..... First, select appropriate values for u and dv. u = and dv = dx Now, find du and v. Treat a and n as constants. du = dx and v = Now, make substitutions in the integration by parts formula and simplify. x" e ax dx = (D - |O dx Finally, apply the constant multiple rule to complete the proof. n ax хе ax dx = dx a xn-1eax n - x"-'eax a ах e a n- 1 nx" -'eax
Use integration by parts to establish the reduction formula. ax хе n 1 ах e е аx dx, a #0 ..... First, select appropriate values for u and dv. u = and dv = dx Now, find du and v. Treat a and n as constants. du = dx and v = Now, make substitutions in the integration by parts formula and simplify. O-SO ax dx = dx e Finally, apply the constant multiple rule to complete the proof. ax ax e dx a n-1 nx' 1 a ax e a in a
Transcribed Image Text:Use integration by parts to establish the reduction formula. ax хе n 1 ах e е аx dx, a #0 ..... First, select appropriate values for u and dv. u = and dv = dx Now, find du and v. Treat a and n as constants. du = dx and v = Now, make substitutions in the integration by parts formula and simplify. O-SO ax dx = dx e Finally, apply the constant multiple rule to complete the proof. ax ax e dx a n-1 nx' 1 a ax e a in a
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