Fractional Parts in 2019

Calculus Level 5

01({1x}{2x})dxx \displaystyle \int_{0}^{1}{\left(\left\{ \frac{1}{x}\right\} \{ 2x \}\right) \frac{dx}{x} }

The above integral is equal to A+lnBCγ,A+\ln{B}-C\gamma, where A,B,CA,B,C are all positive integers.

Find A+B+C.A+B+C.

Note:{} \{ \} denotes the fractional part and γ\gamma denotes the Euler-Mascheroni constant.

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