Does the Integral from e to Infinity of 67/(x(ln(x))^3) Converge?

[tnutty]

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.

Homework Equations

The Attempt at a Solution

i know it converges,

but i got the value

67/2

 

[Unco]

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

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