How do you evaluate [tex] \frac{1}{x\ln x} [/tex] by integration by parts. I tried doing this doing the following:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] u = \frac{1}{\ln x}, du = \frac{-1}{x(\ln x)^{2}}, dv = \frac{1}{x}, v = \ln x [/tex]. So I get:

[tex] \int udv = uv-\int vdu = 1 + \int \frac{1}{x\ln x} = \int \frac{1}{x\ln x} [/tex]. I know the answer is [tex] \ln(\ln x) [/tex]

Thanks

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# Homework Help: Integrartion by parts

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