Hyperbolic Functions

  • Thread starter roam
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  • #1
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1. I am asked to calculate [tex]\int \frac{dx}{cosh(x)}[/tex]



2. Homework Equations



3. The Attempt at a Solution

I know that [tex]\frac{1}{cosh(x)}[/tex] is equivalent to "sech(x)" which by definition is [tex]\frac{2}{e^x+e^{-x}}[/tex].

I'm confused & I don't know which one I need to use for this question:

[tex]\int sech(x) = 2tan{-1}(tanh(\frac{x}{2}))[/tex]

[tex]\int \frac{2}{e^x + e^{-x}} = 2tan^{-1}(e^x)[/tex]

Any help would be greatly appreciated.
 
Last edited:

Answers and Replies

  • #2
316
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The two answers you got only differ by a constant of [tex]\frac{\pi}{2}[/tex]. Recall that the indefinite integral is only defined up to a constant, so both solutions are correct.
 

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