(ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1 16] 01

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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Solve detailly 5ii

5. (i) By using the substitution u = 1+ cosh x,
%3D
cosh-12
tanh x
dx,
1+ cosh x
evaluate
0.
leaving your answer in terms of natural logarithms.
(ii) Show that
d
1
(tanh-1,
dx
%3D
1- x2
|
Hence, or otherwise, show that,
2.
tanh-1x dx =
[271
-In
4.
[16]
Transcribed Image Text:5. (i) By using the substitution u = 1+ cosh x, %3D cosh-12 tanh x dx, 1+ cosh x evaluate 0. leaving your answer in terms of natural logarithms. (ii) Show that d 1 (tanh-1, dx %3D 1- x2 | Hence, or otherwise, show that, 2. tanh-1x dx = [271 -In 4. [16]
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