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Integrating quadratics?

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find the antiderivative of f(x) = x^3(x-2)^2

I factored this out and got

I'm supposed to integrate this. I don't know how. Someone help me please?

BTW, multiple choice options are:

  • Integrating quadratics? -

    Sorry, let me fix that. Multiple Choice options are:

    A: 1/6 x^6 - 4/5 X^5 + x^4 + C
    B: 1/6 x^6 - 4/5 X^5 + 1/4 x^4 + C
    C: x^6 - X^5 + x^4 + C
    D: x^5 - 4x^4 + 4x^3 + C

  • Integrating quadratics? -

    I assume this is a continuation of

    Please pick a "nickname" and stick to it, that way we can follow your posts easier.

    You had asked for the anti-derivative, and I had replied with "integrate"
    That is the more "mathematical" terminology.
    To "integrate" something is the same as finding the "anti-derivative"

    the derivative of 6x^3 + 5x - 2 is 18x^2 + 5
    and the integral or the anti-derivative of 18x^2 + 5 is 6x^3 + 5x

    btw, I had a typo in my expanded form, should have been
    x^5 - 4x^4 + 4x^3 , I am surprised you didn't check that

    so the anti-derivative or the integral of
    x^5 - 4x^2 + 4x^3 is

    (1/6)x^6 - (4/5)x^5 + x^4 + C , where C is a constant

    clearly choice a)

    (differentiate choice a) and see what you get, to verify the answer)

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