# Homework Help: Integration of the natural log

1. Oct 10, 2012

### nusaibahazman

1. how to integrate∫ (ln x)2 /x dx

2. Relevant equations

3. The attempt at a solution

2. Oct 10, 2012

### raopeng

Here it is better to show what you have attempted so far, after all people here are not answer machine. But a hint can be: what is the derivative of ln x?

3. Oct 10, 2012

### SammyS

Staff Emeritus
Although, raopeng suggests that you show what you've attempted, it is actually a part of the rules for posting a thread in the homework help section of this Forum.

raopeng's hint is excellent.

4. Oct 10, 2012

### nusaibahazman

x(ln x)-1+c..i not pretty sure..

5. Oct 10, 2012

### SammyS

Staff Emeritus
The derivative of ln(x) is (1/x) + C .

Do you know integration by substitution?

6. Oct 10, 2012

### nusaibahazman

i know..let u= ln x
then differenciate du/dx= 1/x..

7. Oct 10, 2012

### nusaibahazman

i know..let u= ln x
then differenciate du/dx= 1/x..

8. Oct 10, 2012

### SammyS

Staff Emeritus
After doing all that, what does your integral become, in terms of u ?

9. Oct 10, 2012

### nusaibahazman

u^2 du..right.?

10. Oct 10, 2012

### nusaibahazman

let u= ln x
du/dx= 1/x
dx= x du..
then integrate (u^2/x) x du
then cancel the x...so, integrate the u^2..
right.? i got the idea..tq..