Question Number 133943 by mnjuly1970 last updated on 25/Feb/21
![.......advanced calculus...... prove that: 𝛗= ∫_0 ^( ∞) ((cos(x^2 )−cos(x))/x)dx=(γ/2) γ: euler−mascheroni constant...](https://www.tinkutara.com/question/Q133943.png)
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…….{advanced}\:\:\:\:\:{calculus}…… \\ $$$$\:\:\:\:\:\:{prove}\:\:{that}: \\ $$$$\:\:\:\:\:\:\boldsymbol{\phi}=\:\:\int_{\mathrm{0}} ^{\:\infty} \frac{{cos}\left({x}^{\mathrm{2}} \right)−{cos}\left({x}\right)}{{x}}{dx}=\frac{\gamma}{\mathrm{2}} \\ $$$$\:\:\:\gamma:\:{euler}−{mascheroni}\:{constant}… \\ $$