Evaluating the integral of natural log of the absolute value of x

**soccerballboy20** · April 26th 2009, 05:15 PM

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

**skeeter** · April 26th 2009, 05:38 PM

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 ...

**soccerballboy20** · April 26th 2009, 06:38 PM

what do you mean finish up?

**derfleurer** · April 26th 2009, 06:42 PM

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

You need to finish integrating

**soccerballboy20** · April 27th 2009, 08:09 AM

so would that then result in the answer:

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

??

**derfleurer** · April 27th 2009, 09:16 AM

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

$xlnx - \int dx$

$xlnx - x$ is your answer

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