Euler–Mascheroni constant!

In fact, the last one is:
$${\displaystyle {\int }_1^{+\mathrm{\infty }}\mathrm{d}x(\frac{1}{\lfloor x\rfloor }-\frac{1}{x})=\gamma \approx 0.5772156649}$$

Equivalently,
$${\displaystyle \underset{n\to \mathrm{\infty }}{lim}(\sum _{k=1}^n\frac{1}{k}-\ln n)=\gamma =0.5772156649\dots }$$
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Unsolved problem in mathematics:
Is Euler–Mascheroni constant irrational? If so, is it transcendental?