What is the integral of #ln(sqrt(x))#?

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Answer 1 · 2015-05-02T18:06:00

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]#

don't forget #ln(a^b) = bln(a)#

#[1/2xln(x)-1/2x]#

factorize by #1/2x# and don't forget the constant !

#[1/2x(ln(x)-1)+C]#