Integration involving ${\mathrm{log}}_{2}\left(x\right)$
$\int \frac{\mathrm{ln}\left(2\right){\mathrm{log}}_{2}\left(x\right)}{x}$
I believe $\mathrm{ln}\left(2\right)$ would be considered a constant, so than the equation would then changed to:
$\mathrm{ln}\left(2\right)\int \frac{{\mathrm{log}}_{2}\left(x\right)}{x}$
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Tiberlaue
Since ${\mathrm{log}}_{2}\left(x\right)=\frac{\mathrm{ln}x}{\mathrm{ln}2}$ then your anti-derivative becomes
$\int \frac{\mathrm{ln}x}{x}dx=\int \frac{1}{x}×\mathrm{ln}xdx=\frac{1}{2}\left(\mathrm{ln}x{\right)}^{2}+C$