Calculus - Urgent!!!

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In case this looks familiar, yes, it is a repost. I really need help.

Find the anti-derivitive of
f(x)= x^3(x-2)^2.

Multiple choice gives me the options:
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

I got as far as factoring the original equation into x^5 - 4x^4 + 4x^2. I was told I need to integrate the function. I'm not sure how to do that. My book is NOT clear or helpful, and hasn't been for this whole calculus course.

Please help me understand how my equation can possibly be one of the equations in the A-B-C-D options.

Thank you and God bless you for taking the time to read this, let alone help!

  • Calculus - Urgent!!! -

    Yes, you need to integrate the function.
    I am sure antiderivatives and integration are in your text.

    first multiply it out
    x^3(x-2)^2 = x^3 (x^2 - 4 x + 4)
    = x^5 -4x^4 + 4 x^3 (note that last x^3)

    now in general the integral of x^n dx is (1/n+1)x^(n+1)
    so for example the integral of x^2dx is
    (1/3)x^3 + a constant C
    so here we have
    (1/6)x^6 -(4/5)x^5 + x^4 + C

    Which is answer (a)

  • Calculus - Urgent!!! -


  • Calculus - Urgent!!! -

    Be sure to follow the tutorial links at the bottom left of that link.

  • Calculus - Urgent!!! -

    Ah, thank you so much. Those are very helpful. Yes, anti-derivatives and integrals are in my text, but it is explained in one paragraph. Thanks again!

  • For: "in Need of Help" -

    Now do you see what I meant about switching names in my earlier post

    Both Damon and I spent time answering the same question.

  • Calculus - Urgent!!! -

    I apologize. I didn't see the earlier post, but it won't happen again. Sorry to the both of you.

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