Question:

Find the value of the infinite integral:

$\displaystyle \int^\infty_2 \frac{6}{x^4}dx$

Attempt:

$\displaystyle \int^\infty_2 \frac{6}{x^4}dx$

$\displaystyle = 6x^-4$

$\displaystyle = \frac{6x^{-4+1}}{-4+1}$

$\displaystyle = \frac{6x^{-3}}{-3}$

$\displaystyle = -2x^{-3}$

$\displaystyle = [ -2x^{-3} ]^{\infty}_2$

$\displaystyle = [-2(\infty)^{-3} ] - [-2(2)^{-3} ]$

$\displaystyle = ?$

If there was a number in the infinity position then I would be able to solve it, but with the infinity there. I need help!