Integrating hyperbolic functions


by peripatein
Tags: functions, hyperbolic, integrating
peripatein
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#1
Nov9-12, 07:03 AM
P: 812
Hi,
I am trying to integrate (tanh(x)+coth(x))/((cosh(x))^2)
I am substituting u=tanh(x), du=dx/((cosh(x))^2)
and end up with 1/2(tanh(x))^2 + ln |tanh(x)| + C
which is incorrect. What am I doing wrong??
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peripatein
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#2
Nov9-12, 02:21 PM
P: 812
Does someone have an idea what is stymying my answer?
SteamKing
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#3
Nov9-12, 03:32 PM
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Why did you chose u = tanh(x)? What happens if you expand (tanh(x) + coth (x))?

peripatein
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#4
Nov9-12, 03:42 PM
P: 812

Integrating hyperbolic functions


I used u=tanhx, as 1/(coshx)^2 is its derivative.
Dick
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#5
Nov9-12, 04:36 PM
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Quote Quote by peripatein View Post
Does someone have an idea what is stymying my answer?
There is nothing wrong with your answer. If the book is giving one that looks different it may differ from yours by a constant.
peripatein
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#6
Nov9-12, 04:52 PM
P: 812
Online calculators claim the integral to be -1/2*(coshx)^2 + ln |tanhx| + c.
1/2*(tanhx)^2 (which is the first term in my answer) is not equal to -1/2*(coshx)^2, is it?
Dick
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#7
Nov9-12, 05:00 PM
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Quote Quote by peripatein View Post
Online calculators claim the integral to be -1/2*(coshx)^2 + ln |tanhx| + c.
1/2*(tanhx)^2 (which is the first term in my answer) is not equal to -1/2*(coshx)^2, is it?
Wolfram Alpha gives the first term as -(sechx)^2/2 and that does differ from (tanhx)^2/2 by a constant. What's the constant? Are you sure the online calculator isn't saying -1/(2*(coshx)^2)? You should use more parentheses when you write something like -1/2*(coshx)^2. It's ambiguous.
peripatein
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#8
Nov9-12, 05:21 PM
P: 812
I am not following your argument. Is the answer which Wolfram's calculator yields equal to mine?
My answer is: (0.5)(tanh(x))^2 + ln |tanh(x)| + C
Wolfram's calculator's answer: (-0.5)(sech(x)^2) + ln [tanh(x)] + C
Dick
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#9
Nov9-12, 05:24 PM
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Quote Quote by peripatein View Post
I am not following your argument. Is the answer which Wolfram's calculator yields equal to mine?
My answer is: (0.5)(tanh(x))^2 + ln |tanh(x)| + C
Wolfram's calculator's answer: (-0.5)(sech(x)^2) + ln [tanh(x)] + C
They are only 'equal' if you consider the '+C' part. (tanhx)^2+(sechx)^2=1. Use that identity.
peripatein
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#10
Nov9-12, 05:32 PM
P: 812
I see. Thanks a lot!


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