I'm required to prove that:

$\displaystyle \sinh ^{-1}\left( x \right)\; =\; \ln \left( x\; +\; \sqrt{x^{2}\; +\; 1} \right)$

The furthest I can get is this:

$\displaystyle \sinh ^{-1}\left( x \right)\; =\; \frac{1}{\frac{1}{2}\left( e^{x}-e^{-x} \right)}$

I have no idea what to do Any kind of nudge in the right direction would be greatly appreciated.