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What is the anti derivative `int ln x dx` ?

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What is the anti derivative `int ln x dx` ?

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Posted (Answer #1)

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

Use integration by parts which gives `int u dv = u*v - int v du`

let `u = ln x => du = (1/x)*dx`

and `dv = dx => v = x`

`int ln x dx`

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

=> `x*ln - int 1 dx`

=> `x*ln x - x`

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

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