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

Integrate by parts using the formula , where and .

Combine and .

Combine and .

Combine and .

Multiply and .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

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 .

Rewrite as .

Simplify.

Combine and .

Combine and .

Combine and .

Multiply and .

Multiply by .

Reorder terms.

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