MHB Can You Simplify This Complicated Integral Result?

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The integral result presented is complex, involving logarithmic and arctangent functions related to the golden ratio, φ. Despite attempts to simplify, it appears that the properties of φ do not lend themselves to further reduction, particularly since the fraction representing φ does not appear in the expression. The numeric equivalence to the integral's value has been confirmed, suggesting that the result is accurate. Overall, simplification seems unlikely due to the inherent complexity of the functions involved. Therefore, it may be best to retain the current form of the result.
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I was solving an integral and I got an over complicated result :eek:

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

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 ?
 
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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.
 
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