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

2 Answers

See answer below:
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Dec 1, 2016

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.)