# Thread: Integration Check

1. ## Integration Check

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

$
\frac{e^x+e^{-x}}{e^x-e^{-x}}
$

$
e^x-e^{-x}+c
$

Thank you.

2. 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 $\ln(e^x-e^{-x})+c$

3. The following is completely unnecessary, but true:

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