# Logarithmic Integration

1. Sep 21, 2009

### tjbateh

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

$$\int^{e^2}_{e}$$ $$\frac{1}{xlnx}$$ dx

2. Relevant equations

3. The attempt at a solution

I substituted U= xlnx
So DU= ($$\frac{1}{x}$$dx..........so Du * X = 1dx

From there I am stuck!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Sep 21, 2009

### rock.freak667

so if du =(1/x)dx where u=lnx

what does

$$\int \frac{1}{x lnx} dx$$

change to in terms of u and du?

3. Sep 21, 2009

### tjbateh

$$\frac{du}{u}$$ ?

4. Sep 21, 2009

### rock.freak667

yes so what is

$$\int \frac{1}{u} du = ?$$

5. Sep 21, 2009

### tjbateh

is it just LN (x)??

6. Sep 21, 2009

### rock.freak667

ln(u)

now since you are integrating from e2 to e, what is your integral equal to in terms of x?

7. Sep 21, 2009

### tjbateh

ln e2- ln e

8. Sep 21, 2009

### rock.freak667

No.

If you integrated 1/u du and got ln(u), and u = ln(x). What is ln(u) now?

9. Sep 21, 2009

### tjbateh

it is LN (LN(x))

10. Sep 21, 2009

### rock.freak667

right now so now compute Ln(ln(e2))-Ln(ln(e))

11. Sep 22, 2009

### tjbateh

alright so LN (1/e^2)- LN (1/e) ???

12. Sep 22, 2009

### VietDao29

No no, ln(ln(e2)) is definitely not ln(1/e2).

Now, let's do it step by step then. What is ln(e2)?

13. Sep 22, 2009

### tjbateh

it is 2

14. Sep 22, 2009

### tjbateh

and LN(e) is 1, so it would be LN (2)- LN (1)? Which is .693??

15. Sep 22, 2009

### VietDao29

ln(1) = ln(e0) = 0, so, you can leave it as: ln(2) - ln(1) = ln(2). Taking an approximation is okay, though. :)

16. Sep 22, 2009

### tjbateh

ok so that's the final answer??

17. Sep 22, 2009

### VietDao29

Yup. :)

18. Sep 22, 2009

### tjbateh

Great! Thanks for the help everyone! I just didn't think it made sense to have an LN in another LN, but I guess that works!! Thanks again!