Try integration by parts.
Let u = ln x
du = dx/x
dv = 1/x^2 dx
v = -1/x
Integral of lnx/x^2 = Integral of udv
= uv - Integral of vdu
= -(ln x)/x - Integral of -dx/x^2
Take it from there, but check my work also
how to do the integral of
(ln(x))/(x^2)
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