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 !

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

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