Asked by olga
Evaluate the integral.
from 1 to 5
(ln(x))^2/x^3 dx.
from 1 to 5
(ln(x))^2/x^3 dx.
Answers
Answered by
Steve
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.
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.