# Thread: Evaluating the integral of natural log of the absolute value of x

1. ## Evaluating the integral of natural log of the absolute value of x

Evaluate : *integral sign* ln (abs(x)) dx

2. Originally Posted by soccerballboy20
Evaluate : *integral sign* ln (abs(x)) dx
integration by parts ...

$u = \ln|x|$ ... $du = \frac{1}{x} \, dx$

$dv = dx$ ... $v = x$

$\int \ln|x| \, dx = x\ln|x| - \int x \cdot \frac{1}{x} \, dx$

finish up ...

3. what do you mean finish up?

4. He gave you $x\ln|x| - \int x \cdot \frac{1}{x} \, dx$

You need to finish integrating

5. so would that then result in the answer:

= x ln|x| -(x/2)(ln|x|)

??

6. $x * \frac{1}{x} = 1$

$xlnx - \int dx$

$xlnx - x$ is your answer

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