evaluate ((lnx)^2)^ 1/2 dx

I suppose that you need to find the integral of the
function   such that:

dx

You need to remember that   hence

 
x| dx

You need to use integration by parts, hence you
should write the formula such that:

vdu

You should consider ,
hence Substituting   for u,   for du, x for v and dx
for dv yields:

int |ln x| dx = x*|ln x| - int
x*(dx)/x

dx

x*(|ln x| - 1) +

c

c

Hence, evaluating the integral of function
yields .