- #1

- 327

- 1

## 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

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- Thread starter tnutty
- Start date

- #1

- 327

- 1

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.

i know it converges,

but i got the value

67/2

- #2

- 156

- 0

And I would agree with you...## 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

Using the substitution [tex]u=\ln{x}[/tex], the integral

[tex]\int_e^\infty \frac{1}{x(\ln{x})^3} \, dx[/tex]

becomes

[tex]-\frac{1}{2} \int_1^\infty \frac{1}{u^2} \, du.[/tex]

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