Question

What is `int ln(x)/x`?

Answer 1

`(lnx)^2/(2) +C`

Explanation:

`intln(x)/x dx hArr int[ln(x)*(1/x)]dx`

Can be solve by u-substitution

Let `" " u= ln (x) " " " " " (1) " "`

`" " " " du = 1/x dx " " " " (2)" "`

equal to `dx` in the original problem

Let substitute that back into the original
`int u du = (u^2)/2 +C " " " " " (3)"`

Re-substitute `u= ln x` into solution above (3)

Final answer: `(lnx)^2/(2) +C`

I hope this help :)