Simplifying ln(exp(-a) + exp(a)) - Need Help with Homework

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Homework Statement


Hey, does anyone know how to further simplify this:



Homework Equations


ln(exp(-a) + exp(a))?


The Attempt at a Solution

 
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There is no such rule as ln(x+y)=lx+lny if that is what you wanted to know. The most I can think of is that cosh(x)= 1/2(ex+e-x)
 


Thank you, this is good. I was after a trig simplification.
I knew one for 2cos(x) = exp(-ix) + exp(ix) but couldn't remember one without the imaginary.
Ta!
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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