How do you find the indefinite integral of #int (lnx)^2/x#?

1 Answer
Nov 4, 2016

# int (lnx)^2/x dx = 1/3(lnx)^3 + C#

Explanation:

This is a straight forward with the appropriate substitution

Let # u = lnx => (du)/dx=1/x #, so #int ...du=int...1/xdx#

So Then,
# int (lnx)^2/x dx = int u^2du#
#:. int (lnx)^2/x dx = 1/3u^3 + C#
# :. int (lnx)^2/x dx = 1/3(lnx)^3 + C#