What is the indefinite integral of $ln(sqrt(x)) dx$ ?

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Answer 1 · 2016-08-08T22:14:13

$1/2(xlog_e(x)-x) + C$

$log_e(sqrt(x))= 1/2log_e(x)$ and

$d/(dx)(x log_e(x))=log_e(x) + 1$

then

$int log_e(sqrt(x))dx = 1/2 int log_e(x) dx= 1/2(xlog_e(x)-x) + C$

What is the indefinite integral of ln(sqrt(x)) dxln(sqrt(x)) dx?