1. Integration

Hi. I'm trying to integrate $\displaystyle \int\frac{1+lnx}{xlnx}\ dx$ I think it's of the form f'(x)/f(x) so shouldn't the answer be ln(xlnx)? This is not the answer in the back of the book however.

2. Split it up into two integrals.

3. so i get $\displaystyle \int\frac{1}{x} + \int\frac{1}{lnx}$ but then how do I integrate 1/lnx dx? if I use substitution the dx gets messy.

4. Originally Posted by flashylightsmeow
so i get $\displaystyle \int\frac{1}{x} + \int\frac{1}{lnx}$ but then how do I integrate 1/lnx dx? if I use substitution the dx gets messy.
Surely, $\displaystyle \displaystyle \frac{1+\ln{x}}{x\ln{x}} \ne \frac{1}{x}+\frac{1}{\ln{x}}$?

5. sorry, 1/x + 1/xlnx, is that correct?

6. Originally Posted by flashylightsmeow
sorry, 1/x + 1/xlnx, is that correct?
Yes, note that $\displaystyle \displaystyle \frac{1}{x\ln{x}} = \frac{1/x}{\ln{x}}$.

7. Yes, $\displaystyle \dfrac{1 + \ln x}{x\ln x} = \dfrac{1}{x} + \dfrac{1}{x\ln x}$.

Edit: I was a little slow. :P

8. Originally Posted by NOX Andrew
Edit: I was a little slow. :P
Same minute! Talk about luck on my part!

9. Thanks guys.