integration by u substitution..I think

[tgrrrrr1976]

the problem is the integral of 1/(xlnx)

there's no simple way to just anti-differentiate this is there? it seems like I would have to use u substitution, but have no clue how to go about it...

 

[BigGlenntheHeavy]

\(\displaystyle \int\frac{dx}{xln|x|}, \ Let \ u \ = \ ln|x|, \ then \ du \ = \ \frac{dx}{x}\)

\(\displaystyle Hence, \ we \ have \ \int\frac{du}{u} \ = \ \int u^{-1}du \ = \ ln|u|+C \ = \ ln(ln|x|)+C\)

 

[tgrrrrr1976]

thanks, I always try to either over-complicate or jump ahead and I get mixed up, you cleared it up for me