Improper Integrals with u sub and integration by parts ?

[Jay J]

Homework Statement

The integral from 1 to infinity of (lnx)/(x) dx

Homework Equations

U substitution and integration by parts

The Attempt at a Solution

Cant decide what to use as my "u" . . can anyone help with this part ?

-Jay J-

 

[kreil]

this doesn't really require integration by parts, just a u-substitution:

$$\int \frac{ln(x)}{x}=\int u du = \frac{1}{2}u+ C= \frac{1}{2}(ln(x))^2+C$$

here you take u = ln(x) and differentiate to get, du = 1/x dx.

 

[Jay J]

ok i understand the whole u substitution part but then i have to determine whether or not the integral is divergent or convergent and if its convergent i have 2 evaluate it . .. how would you do that ?

-Jay J-

 

[Dick]

Evaluate the integral between x=0 and x=M and let M approach infinity. What do you conclude?