## Integrating hyperbolic functions

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??
 Does someone have an idea what is stymying my answer?
 Recognitions: Homework Help Why did you chose u = tanh(x)? What happens if you expand (tanh(x) + coth (x))?

## Integrating hyperbolic functions

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

Recognitions:
Homework Help
 Quote by peripatein 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.
 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?

Recognitions:
Homework Help
 Quote by peripatein 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.
 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

Recognitions:
Homework Help