Question

Determine whether the improper integral converges or diverges, and find the value of each that converges.

Answer 1

Answer:

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 ∞