# Integrating hyperbolic functions

by peripatein
Tags: functions, hyperbolic, integrating
 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??
 P: 818 Does someone have an idea what is stymying my answer?
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,746 Why did you chose u = tanh(x)? What happens if you expand (tanh(x) + coth (x))?
 P: 818 Integrating hyperbolic functions I used u=tanhx, as 1/(coshx)^2 is its derivative.
HW Helper
Thanks
P: 25,235
 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.
 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?
HW Helper
Thanks
P: 25,235
 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.
 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