# Improper Integrals with u sub and integration by parts ?

1. Apr 12, 2009

### Jay J

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

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

2. Relevant equations
U substitution and integration by parts

3. The attempt at a solution
Cant decide what to use as my "u" . . can any one help with this part ?

-Jay J-

2. Apr 12, 2009

### 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.

3. Apr 12, 2009

### 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-

4. Apr 12, 2009

### Dick

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