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What is the integral `int ln x dx` 

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asicannot41 | Student | eNoter

Posted July 29, 2012 at 5:30 AM via web

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What is the integral `int ln x dx` 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 29, 2012 at 5:37 AM (Answer #1)

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The integral `int ln x dx` has to be determined.

This is done using integration by parts which states: `int u*v' = u*v - int u'*v`

Let `v = x` and `u = ln x` , `v' = 1` and `u' = 1/x`

`u*v' = ln x*1 = ln x`

`int ln x dx = ln x*x - int x*(1/x) dx`

=> `int ln x dx = ln x*x - x + C`

The integral `int ln x dx = ln x*x - x + C`

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