integral

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December 2nd 2009, 06:32 PM
stevo970

integral

Integral of $<br /> (e^x-e^-x)/(e^x+e^-x)<br />$

I have tried adding the conjugate to the top and bottom but don't know where to go from there. Should I continue that or try a different technique?
December 2nd 2009, 06:54 PM
Soroban

Hello, stevo970!

If you look at it the right way, it's easy . . .

Quote:

$\int\frac{e^x-e^{-x}}{e^x+e^{-x}}\,dx$

Let $u$ = the denominator.

We have: . $\begin{array}{ccc}u &=& e^x + e^{-x} \\ du &=& (e^x - e^{-x})\,dx \end{array}$

Hence, we have: . $\int\frac{du}{u}$

Got it?
December 3rd 2009, 11:42 AM
stevo970

wow ok thank you
December 3rd 2009, 12:06 PM
hmmmm

also noting that this is (sinh(x))/(cosh(x)) may make this become clearer

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