Improper Integrals - Infinite Intervals

[forestmine]

Improper Integrals -- Infinite Intervals

Homework Statement

Evaluate the integral.

(from e to infinity) ∫(25/x(lnx)^3)dx

Homework Equations

The Attempt at a Solution

I know that for evaluating improper integrals, you can take the limit as t approaches infinity of the given integral, but my problem is in evaluating the integral itself.

25 comes out of the integrand, and so I'm left with dx/x(lnx)^3, and this is where I'm confused. I'm guessing integration by parts is necessary to properly evaluate this, but I'm not entirely sure. I tried setting u = (lnx)^-3, which gives me du=-3lnx/x*dx, but then I'm left with dv=xdx, so v=1/2x^2, but based on the solution, I don't believe I'm at all headed in the right direction.

Any help would be greatly appreciated!

 

[ehild]

I'm guessing integration by parts is necessary to properly evaluate this,

Use the substitution u=ln(x) instead.


ehild

 

[forestmine]

I did exactly that and it works out perfectly.

Thanks a lot!