How do you integrate $int x^2lnabs(x)$ by integration by parts method?

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How do you integrate $int x^2lnabs(x)$ by integration by parts method?

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Answer 1 · 2018-02-02T14:38:08

$1/9x^3(3ln(x)-1)$

Explanation:

Integration by parts:
$int(v'*u)=u*v-int(v*u')$
Let $u=ln(x), u'=1/x$
and $v'=x^2,v=1/3x^3$
$int(x^2ln(x))$
$=1/3x^3ln(x)-int(1/3x^(cancel(3) 2)*1/cancel(x)$
$=1/3x^3ln(x)-1/9x^3$
$=1/9x^3(3ln(x)-1)$

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How do you integrate $int x^2lnabs(x)$ by integration by parts method?

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How do you integrate $int x^2lnabs(x)$ by integration by parts method?