Evaluate the integral.

from 1 to 5
(ln(x))^2/x^3 dx.

1 answer

let
u = (lnx)^2
dv = x^-3 dx

du = 2lnx/x dx
v = -1/2 x^-2

∫u dv = uv - ∫v du
∫(lnx)^2/x^3 dx = -(lnx)^2/(2x^2) - ∫(-lnx)/(x^3) dx

Now repeat with u=lnx and you will be left with just a power of x to integrate.