# Homework Help: Integral from e to infinity

1. Feb 20, 2009

### tnutty

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

3. The attempt at a solution

i know it converges,

but i got the value

67/2

2. Feb 21, 2009

### Unco

Re: divergent/convergent

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

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