Question

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

Answer 1

`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)`