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What is the integral of ##ln(sqrt(x))##?
By part :
##intln(sqrt(x))dx##
##du = 1## ##u = x##
##v = ln(sqrt(x))## ##dv = 1/(2x)##
##[xln(sqrt(x))]-1/2intdx##
##[xln(sqrt(x))-1/2x]##
##[1/2x(ln(x)-1)+C]##