Let denote the Euler – Mascheroni constant. Prove that

**Solution**

Let us consider the following

It is known that . Also, the Mellin transform of is known to be

Hence

On the other hand

What we are seeking is .

and the result follows.

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# A curious logarithmic and trigonometric integral

Let us consider the following
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Let denote the Euler – Mascheroni constant. Prove that

**Solution**

It is known that . Also, the Mellin transform of is known to be

Hence

On the other hand

What we are seeking is .

and the result follows.