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Integrating hyperbolic functions 
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#1
Nov912, 07:03 AM

P: 818

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?? 


#2
Nov912, 02:21 PM

P: 818

Does someone have an idea what is stymying my answer?



#3
Nov912, 03:32 PM

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Why did you chose u = tanh(x)? What happens if you expand (tanh(x) + coth (x))?



#4
Nov912, 03:42 PM

P: 818

Integrating hyperbolic functions
I used u=tanhx, as 1/(coshx)^2 is its derivative.



#5
Nov912, 04:36 PM

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#6
Nov912, 04:52 PM

P: 818

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? 


#7
Nov912, 05:00 PM

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#8
Nov912, 05:21 PM

P: 818

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 


#9
Nov912, 05:24 PM

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#10
Nov912, 05:32 PM

P: 818

I see. Thanks a lot!



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