Question

`int 1/(x(log x)^2) dx` is equal to ______.

Options

• 2 log (log x) + c

• `-1/(log x) + c`

• `(log x)^3/3 + c`

• `3/(log x)^3 + c`

Answer 1

`int 1/(x(log x)^2) dx` is equal to `bbunderline(-1/(log  x) + c)`.

Explanation:

Let I = `int 1/(x(log x)^2) = dx`

log x = t ⇒ `1/xdx = dt`

∴ I = `int dt/t^2 = -1/t + c`

Thus, I = `-1/(log x) + c`