# Calc 2 simple integration i'm stuck on

1. May 3, 2013

### marc017

My first post lets see if i did this typing right, if not please forgive me...

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

$$\int \frac{(1+ln x)^2}{x}\,dx$$

2. Relevant equations

Trying to attack it by using substitution..

3. The attempt at a solution

Using...
u = 1 + ln(x) , du = 1/x

\begin{align} \int \frac{(1+ln x)^2}{x}\,dx \\ &= \int (u)^2\,du \\ &= \frac{u^3}{3} + C \\ &= \frac{(1+ln x)^3}{3} + C \\ \end{align}

Where did I go wrong?

Last edited: May 3, 2013
2. May 3, 2013

### Skins

What happens if you instead let u = lnx ? Work it out and see what happens. Does the result look more like the answer in your textbook ?

Also, what makes you think your first answer is wrong ? Try expanding $(1 + lnx)^3$ in your first answer What does the result look like ? Does it look like the answer in the textbook or the answer your instructor provided ?

Last edited: May 3, 2013
3. May 3, 2013

### marc017

Thank you skins.

4. May 3, 2013

### SammyS

Staff Emeritus
It looks good to me.

To check it, take the derivative with respect to x.

Also, as skins has suggested, expand $\ (1+\ln(x))^3\ .$

Don't forget the constant of integration that is in one solution may not match constant of integration in another solution. In particular, if C is a constant, then C + 1 is also a constant.

5. May 3, 2013

### Skins

Thank you, you're welcome. As it turned out your answer was correct all along, It was just that the form of your final answer was probably different than what showed in your textbook or on the blackboard. But it was still correct nonetheless.