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Properties of Indefinite Integrals

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Consider the following statements regarding the integration of the function 4x2+8x4x^2+8x.

I. The indefinite integral ∫(4x2+8x) dx\int (4x^2+8x) \,dx evaluates to 4x33+4x2+C\frac{4x^3}{3}+ 4x^2+ C.

II. The derivative of 4x33+4x2+C\frac{4x^3}{3}+ 4x^2+ C with respect to xx is 4x2+8x4x^2+8x.

III. The expression 4x2+8x4x^2+8x can be factored as 4x(x+2)4x(x+2). Applying an appropriate substitution to this factored form will result in an antiderivative that differs from the one in statement I by only a constant.

Which of the statements above are true?

A

I, II, and III

B

I only

C

II and III

D

I and III

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