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

Question

11772 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-01T23:15:44

See answer below:
enter image source here

Answer 2 · 2016-12-01T23:24:01

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

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.)

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