Question

What is the antiderivative of `ln(x)/x`?

Answer 1

`ln^2(x)/2 +C`

Explanation:

`I=int lnx/x dx`

Let `u=lnx`

`(du)/dx = 1/x -> dx=x du` [Standard differential]

`:. I= int u/x * x du = int u du`

`= u^2/2` [Power rule]

Undo u substitution:

`I = ln^2 (x)/2 +C`