Question

How do you integrate `int 1/(x(lnx)^3)` by parts?

Answer 1

See answer below:

Answer 2

If I had a choice, I would not use parts, I would use the substitution `u = (lnx)^-3`

Explanation:

If I was told I needed to use parts, I would take `u = 1` so `du = 0dx` and `dv = (lnx)^-3 1/x dx` so `v = -1/2(lnx)^-2` (by sustitution).

`uv-int v du = -1/(2(lnx)^2) - int 0 dx`

`= -1/(2(lnx)^2) +C`

(I know it isn't " really" integration by parts.)