3. Define ln(x) = f₁du. Fix x € (-1, 1). Use u-substitution to prove that Cx x [+1=² - In (1+²) -dt = ln t
3. Define ln(x) = f₁du. Fix x € (-1, 1). Use u-substitution to prove that Cx x [+1=² - In (1+²) -dt = ln t
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:3. Define ln(x) = f₁du. Fix x € (-1, 1). Use u-substitution to prove
that
Hint: Use
11
-X
rx 1
1-t
-dt
-dt = ln
1 + x
1- x
= L_₁ ₁ ² -₁ ª ² + √²
-dt-
1-t
-X
1
- dt.
1-t
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