Mathematics: Determine whether the improper integral converges or diverges, and find the value of each that converges. ∫^[infinity]_2 1/x ln x dx

Determine whether the improper integral converges

dianelys3083p5spb5

15.01.2022

Diverges

Step-by-step explanation:

We can solve this by using integral by parts:

Let

u=lnx dv=(1/x)dx

du=(1/x)dx v=lnx

$\int\limits {lnx/x} \, dx = (lnx)^2-\int\limits {lnx/x} \, dx$

We can add

$\int\limits {lnx/x} \, dx$ to both sides

$\int\limits{lnx/x} \, dx = (1/2)\cdot{(lnx)^2}$

We can evaluate the limit between 2 and infinity.

If x tends to infinity the limit will be infinity and therefore the integral diverges to ∞

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nickddj12

11.06.2020

Stop asking for answers you dumb fu(ker

Step-by-step explanation: suk me p.p

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