Evaluate integral of x^2 natural log of x with respect to x

Evaluate integral of x^2 natural log of x with respect to x
Integrate by parts using the formula , where and .
Simplify.
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Combine and .
Combine and .
Combine and .
Multiply and .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Since is constant with respect to , move out of the integral.
By the Power Rule, the integral of with respect to is .
Simplify the answer.
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Rewrite as .
Simplify.
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Combine and .
Combine and .
Combine and .
Multiply and .
Multiply by .
Reorder terms.
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