Question

How do you integrate `intlnx/x` using substitution?

Answer 1

`intlnx/xdx = 1/2ln^2x+a`

Explanation:

Let `u = lnx` then `(du)/dx=1/x` so we can write `du=1/xdx`

Substituting into the integral we get:

`\ \ \ \ \ intlnx/xdx = int(lnx)(1/xdx)`
`:. intlnx/xdx = int(u)(du)`
`:. intlnx/xdx = intudu`
`:. intlnx/xdx = 1/2u^2+a`

And replacing `u` we get:

`\ \ \ \ \ intlnx/xdx = 1/2ln^2x+a`