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To integrate x^3 + 2x^2 + x, use the power rule and the constant multiple rule.

First, apply the power rule to integrate x^3, which gives (1/4)x^4. Then, apply the power rule again to integrate 2x^2, which gives (2/3)x^3. Finally, apply the power rule and the constant multiple rule to integrate x, which gives (1/2)x^2.

Therefore, the integral of x^3 + 2x^2 + x is:

(1/4)x^4 + (2/3)x^3 + (1/2)x^2 + C

where C is the constant of integration.

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