What is the antiderivative of $lnsqrt( 5 x )$ ?

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Answer 1 · 2016-01-09T01:40:36

$I = (x(ln(5)+ln(x) - 1))/2 + c$

$I = intln(sqrt(5x))dx$

Using log properties

$I = 1/2int(ln(5) + ln(x))dx$

$I = (xln(5))/2 + 1/2intln(x)dx$

For the last integral say $u = ln(x)$ so $du = 1/x$ and $dv = 1$ so $v = x$

$I = (xln(5))/2 + 1/2(ln(x)x - intx/xdx)$
$I = (x(ln(5)+ln(x) - 1))/2 + c$

What is the antiderivative of lnsqrt( 5 x )lnsqrt( 5 x )?