What is the antiderivative of ${(ln x)}^{2}$ $(ln x)^2$ ?

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Answer 1 · 2016-01-13T10:32:11

$x {(ln x)}^{2} - 2 x ln x + 2 x + C$ $x(ln x)^2 - 2x ln x + 2x +C$

Let $u = {(ln x)}^{2}$ $u=(ln x)^2$
$d v = d x$ $dv = dx$
$v = x$ $v=x$
$d u = 2 (ln x) \cdot \frac{d x}{x}$ $du = 2(ln x)* dx/x$

What is the antiderivative of (lnx)2(ln x)^2?