Properties of Indefinite Integrals
Consider the following statements regarding the integration of the function $$4x^2+8x$$.
I. The indefinite integral $$\int (4x^2+8x) \,dx$$ evaluates to $$\frac{4x^3}{3}+ 4x^2+ C$$.
II. The derivative of $$\frac{4x^3}{3}+ 4x^2+ C$$ with respect to $$x$$ is $$4x^2+8x$$.
III. The expression $$4x^2+8x$$ can be factored as $$4x(x+2)$$. 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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