Question

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

Answer 1

`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`