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.
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Split it up into two integrals.
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.
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, $\displaystyle \displaystyle \frac{1+\ln{x}}{x\ln{x}} \ne \frac{1}{x}+\frac{1}{\ln{x}}$?
sorry, 1/x + 1/xlnx, is that correct?
Originally Posted by flashylightsmeow sorry, 1/x + 1/xlnx, is that correct? Yes, note that $\displaystyle \displaystyle \frac{1}{x\ln{x}} = \frac{1/x}{\ln{x}}$.
Yes, $\displaystyle \dfrac{1 + \ln x}{x\ln x} = \dfrac{1}{x} + \dfrac{1}{x\ln x}$. Edit: I was a little slow. :P
Originally Posted by NOX Andrew Edit: I was a little slow. :P Same minute! Talk about luck on my part!
Thanks guys.
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