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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