What is the integral `int 1/(x*ln(x)) dx`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The integral `int 1/(x*ln x) dx` has to be determined.

Let `ln x = y`

`dy = (1/x)*dx`

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

=> `int (1/y) dy`

=> `ln y`

substituting `y = ln x`

=> `ln(ln x)`

The integral `int 1/(x*ln x) dx = ln(ln x) + C`

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