Integration Check

**bearhug** · February 21st 2010, 12:09 PM

I attempted to solve this on my own...please let me know if I am correct

$<br /> \frac{e^x+e^{-x}}{e^x-e^{-x}}<br />$

my answer:
$<br /> e^x-e^{-x}+c<br />$

Thank you.

**Moo** · February 21st 2010, 12:11 PM

Hello,

Note that the numerator is the derivative of the denominator. So you have something in the form u'/u. Thus the integral would give $\ln(e^x-e^{-x})+c$

**Random Variable** · February 21st 2010, 12:20 PM

The following is completely unnecessary, but true:

$\int \frac{e^{x}+e^{-x}}{e^{x}-e^{-x}} \ dx = \int \coth{x} \ dx = \ln ({\sinh {x}}) + C = \ln \Big(\frac{e^{x}-e^{-x}}{2}\Big) + C = \ln (e^{x}-e^{-x}) + B$

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