What is the integral `int ln x/x dx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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

Let `ln x = t`

`dt/dx = 1/x => (1/x)* dx = dt`

`int ln x/x dx`

= `int t dt`

= `t^2/2`

Substitute `t = ln x`

= `(ln x)^2/2`

The integral `int ln x/x dx = (ln x)^2/2 + C`