Use integration by parts to establish the reduction formula: [(In x)" daz = 2(lnx)" - n [ (in z)-¹da: To begin the integration by parts, let u = and du = =dz and v=[ leads immediately to the above reduction formula. Evaluating du = Now apply the reduction formula to the problem: (Inz)ºdz. Getting the final result would be tedious, requiring 9 applications of the reduction formula. So for simplicity just give the result of applying the reduction formula one time. (In a)'da is simplified to 0+/Odz dx +C.

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:
To begin the integration by parts, let u =
Evaluating du = de and v =
-0
leads immediately to the above reduction formula.
[(lnx) dx = x(lnx)" - n f (lnx)n-1 da:
and du =
dx.
Now apply the reduction formula to the problem: (In x) dx. Getting the final result would be tedious, requiring 9 applications of the reduction formula.
So for simplicity just give the result of applying the reduction formula one time. (In 2) da is simplified to
+10
dx +C.
Transcribed Image Text:Use integration by parts to establish the reduction formula: To begin the integration by parts, let u = Evaluating du = de and v = -0 leads immediately to the above reduction formula. [(lnx) dx = x(lnx)" - n f (lnx)n-1 da: and du = dx. Now apply the reduction formula to the problem: (In x) dx. Getting the final result would be tedious, requiring 9 applications of the reduction formula. So for simplicity just give the result of applying the reduction formula one time. (In 2) da is simplified to +10 dx +C.
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