# Proving a Sinh(x) expression to be an integer

1. Sep 16, 2009

### supersticky99

Prove or disprove: sinh2(ln($$\sqrt{}2$$+$$\sqrt{}3$$)) is an integer

Obviously, I used my calc to figure out that the answer is 2. Proving it w/o a calc is hard though.

3. The attempt at a solution

I've tried rewriting sinh2 as (1/4)(e2x+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?....

2. Sep 16, 2009

### ehild

Use the identity

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

to eliminate exp and ln.

ehild