Proving a Sinh(x) expression to be an integer

[supersticky99]

Prove or disprove: sinh²(ln($$\sqrt{}2$$+$$\sqrt{}3$$)) is an integerObviously, I used my calc to figure out that the answer is 2. Proving it w/o a calc is hard though.

The Attempt at a Solution

I've tried rewriting sinh² as (1/4)(e^2x+e^-2x-2) and after all the substitutions and log rules I get (1/4)(ln($$\sqrt{}2$$+$$\sqrt{}3$$)+1/(ln($$\sqrt{}2$$+$$\sqrt{}3$$))-2)

what now?...

 

[ehild]

Use the identity

$$\exp{(\ln{x})}=x$$

to eliminate exp and ln.

ehild