advanced-math-two-simple-and-nice-integrals-prove-that-1-0-sin-e-x-ln-x-x-dx-0-2-0-sin-x-2-2-l

Question Number 122713 by mnjuly1970 last updated on 19/Nov/20

\dots a d v a n c e d m a t h \dots

t w o s i m p l e a n d n i c e i n t e g r a l s :

p r o v e t h a t ::

Ω_{1} = \int_{0}^{\infty} \frac{s i n (e^{- γ} x) l n (x)}{x} d x = 0

Ω_{2} = \int_{0}^{\infty} \frac{s i n (x^{\frac{\sqrt{2}}{2}}) l n (x)}{x} d x = - π γ

n o t e :: γ : E u l e r - m a s c h e r o n i

c o n s t a n t .

. m . n .