find-e-2-dt-tln-t-ln-ln-t-

Question Number 40156 by maxmathsup by imad last updated on 16/Jul/18

f i n d \int_{e^{2}}^{+ \infty} \frac{d t}{t l n (t) l n (l n (t)}

Commented by maxmathsup by imad last updated on 21/Jul/18

l e t I = \int_{e^{2}}^{+ \infty} \frac{d t}{t l n (t) l n (l n (t))} c h a n g e m e n t l n (l n (t)) = x g i v e

d x = \frac{1}{t l n (t)} d t \Rightarrow \frac{1}{t l n (t)} = \frac{d x}{d t} \Rightarrow

I = \int_{l n (2)}^{+ \infty} \frac{d x}{x} = {l i m}_{ξ \to + \infty} \int_{l n (2)}^{ξ} \frac{d x}{x} = {l i m}_{ξ \to + \infty} {[l n ∣ x ∣]}_{l n (2)}^{ξ} = {l i m}_{ξ \to + \infty} l n (\frac{ξ}{l n (2)})

= + \infty t h e n t e g r a l i s d i v e r g e n t . ?

=

Answered by tanmay.chaudhury50@gmail.com last updated on 16/Jul/18

y = l n {l n (t)}

d y = \frac{d t}{t l n t}

\int_{l n 2}^{\infty} \frac{d y}{y}

∣ l n y ∣_{l n 2}^{\infty} = l n \infty - l n (l n 2) p l s c h r c k \dots