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Very complicated result


Well-known member
MHB Math Helper
Jan 17, 2013
I was solving an integral and I got an over complicated result :eek:

\(\displaystyle \frac{1}{2}\log^2\left(\phi\right)-\frac{1}{4}\log^2\left( \frac{1+\phi }{4}\right)-\arctan^2\left(\sqrt{\phi}\right)\)

where $\phi$ is the golden ratio .

The numeric value proved an equivalence to the value of the integral .

Can anybody simplify it a little bit , or should I leave it like this ?


Indicium Physicus
Staff member
Jan 26, 2012
It doesn't look to me like you could simplify it. $\phi$ does not have nice properties, so far as I know, with the fractions you have there. It is true that
$$ \phi=\frac{1+\sqrt{5}}{2},$$
but you don't have that fraction showing up anywhere.