How do you integrate #int x^2lnx# by parts from #[1,2]#?

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How do you integrate #int x^2lnx# by parts from #[1,2]#?

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Answer 1 · 2016-12-28T11:41:27

#int_1^2x^2lnxdx=8/3ln2-7/9#

Explanation:

#int_1^2x^2lnxdx=int_1^2lnx d(x^3/3) = [x^3/3lnx]_1^2 - int_1^2x^3/3d(lnx) = 8/3ln2-int_1^2x^3/3(dx)/x=8/3ln2-int_1^2x^2/3dx=8/3ln2-[x^3/9]_1^2=8/3ln2-7/9#

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How do you integrate #int x^2lnx# by parts from #[1,2]#?

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