# Integral from e to infinity

## Homework Statement

integral [from e to infinity of ] 67 / (x(ln(x))^3)

read as the integral from e to infinity of

67 divided by x times cubed lnx.

## The Attempt at a Solution

i know it converges,

but i got the value

67/2

## Homework Statement

integral [from e to infinity of ] 67 / (x(ln(x))^3)

read as the integral from e to infinity of

67 divided by x times cubed lnx.

## The Attempt at a Solution

i know it converges,

but i got the value

67/2
And I would agree with you...

Using the substitution $$u=\ln{x}$$, the integral

$$\int_e^\infty \frac{1}{x(\ln{x})^3} \, dx$$

becomes

$$-\frac{1}{2} \int_1^\infty \frac{1}{u^2} \, du.$$