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Determine all primitive functions

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  1. Sep 3, 2016 #1
    1. The problem statement, all variables and given/known data

    Determine all primitive functions for the function:

    2x(x^2+3)^4

    2. The attempt at a solution

    When i expanded i got the primitive to be:

    2(x^9/9)+3x^8+18x^6+54x^4+81x^2


    But this was wrong. I am not sure I have understood the question. Help?
     
  2. jcsd
  3. Sep 3, 2016 #2

    Mark44

    Staff: Mentor

    I have moved this thread, as it is not a precalculus problem.

    Apparently the problem asks you to find all antiderivatives of 2x(x2 + 3)4. In other words, carry out this integration: ##\int 2x(x^2 + 3)^4 dx##. The answer should have a highest degree term of x10. Don't forget the constant of integration.
    Instead of expanding the binomial in parentheses, think about a simple substitution that you can do.
     
  4. Sep 3, 2016 #3
    One possible substitution is 2x(z)^4

    But I am not sure how to proceed from here...
     
  5. Sep 3, 2016 #4

    Mark44

    Staff: Mentor

    If z = x^2 + 3, what is dz?
    A very simple substitution will work, and you're on the right track,
    When you use substitution to evaluate an integral, you're using the chain rule in reverse.
     
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