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JH
Numerade Educator

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Problem 75 Medium Difficulty

Evaluate the integral.

$ \displaystyle \int \frac{dx}{x \ln x - x} $

Answer

$\ln |\ln x-1|+C$

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Video Transcript

Let's start off here by just factoring the denominator. So we pull out of X and then let's do it. Use up here, you equals ln that do you is one over x gx so we can write this in a girl is one over humanise one, Do you? They do. You is equal to one over x t x. So that's taking care of this part right here, Phil. And then the U minus. Juan is taking care of the Ellen minus one. Now this we could integrate. That's just natural log. You minus one. Plus he now, if this minus one was bothering you, you can do it. A substitution here and you'LL arrive at this answer and then natural log. And finally, just come back up here and replace you with natural log of X. So we have natural lot Absolute value. Natural log X minus one closer constancy. And that's our final answer.