Integration of the natural log

[nusaibahazman]

1. how to integrate∫ (ln x)² /x dx

Homework Equations

The Attempt at a Solution

 

[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?

 

[SammyS]

1. how to integrate∫ (ln x)² /x dx

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?

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.

 

[nusaibahazman]

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

 

[SammyS]

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

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

Do you know integration by substitution?

 

[nusaibahazman]

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

 

[nusaibahazman]

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

 

[SammyS]

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

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

 

[nusaibahazman]

u^2 du..right.?

 

[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..