Substitute u = ln(x) Substitute v = Ա 2 Problem: In²(x) /x = dx du 1 dx x 26 x = √x In²(x) = u² = fu²e³ du ... or choose an alternative: Substitute √ du 1 du 2 = (steps) →→→→dx = -8 8/v²e- (steps) v²e" dv = x du, use: →→du = -2 dv:

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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How does the squareroot of x=e^(u/2)?

Substitute u = ln(x) –
Substitute v =
du 1
dx x
24
√x = e²
In²(x) = u²
= fu³e² du
... or choose an alternative:
Substitute √
1
2
-8/v²e ºd
du
U
2
Problem:
In²(x) dx
√x
=
du
du
== (steps)
=
→→dx= x du, use:
(steps) du = −2 dv:
Transcribed Image Text:Substitute u = ln(x) – Substitute v = du 1 dx x 24 √x = e² In²(x) = u² = fu³e² du ... or choose an alternative: Substitute √ 1 2 -8/v²e ºd du U 2 Problem: In²(x) dx √x = du du == (steps) = →→dx= x du, use: (steps) du = −2 dv:
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