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Antiderivative math homework help

  1. Apr 14, 2010 #1
    1. The problem statement, all variables and given/known data

    [tex]\int(2x^2+1)^7[/tex]

    2. Relevant equations



    3. The attempt at a solution
    u=2x^2+1
    du=4xdx
    u7 (1/4x)du
    I am stuck... I don't know what to do next...
     
  2. jcsd
  3. Apr 14, 2010 #2

    Mark44

    Staff: Mentor

    Re: Antiderivative

    Try to remember to put in the differential...
    Substitution won't work in this case, which you already found out. If you expand [itex]\int(2x^2+1)^7[/itex], you'll get a polynomial that you can integrate pretty easily.
     
  4. Apr 14, 2010 #3
    Re: Antiderivative

    wow, so i have to expand everything out? (2x^2+1)^7
    that's a lot
    is there any other way to do it?
     
  5. Apr 14, 2010 #4

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
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    Re: Antiderivative

    The x2 suggests a trig substitution might work.

    Edit: Actually, that looks to be more of a pain than just multiplying the polynomial out.

    Hint: Use the binomial theorem.
     
  6. Apr 14, 2010 #5

    Mark44

    Staff: Mentor

    Re: Antiderivative

    Nope, I don't think so, at least no way that's not a lot more complicated.
     
  7. Apr 14, 2010 #6
    Re: Antiderivative

    Is using a symbolic processor cheating? From Maxima ...

    ratsimp((2*x^2+1)^7);

    [tex]128\,{x}^{14}+448\,{x}^{12}+672\,{x}^{10}+560\,{x}^{8}+280\,{x}^{6}+84\,{x}^{4}+14\,{x}^{2}+1[/tex]
     
  8. Apr 14, 2010 #7

    Mark44

    Staff: Mentor

    Re: Antiderivative

    Probably not, but will you have one available during a test?
     
  9. Apr 14, 2010 #8
    Re: Antiderivative

    No , I don't think so.
     
  10. Apr 15, 2010 #9

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Re: Antiderivative

    It does help to know the "binomial theorem":

    [tex](a+ b)^n= \sum_{i=0}^n \begin{pmatrix}n \\ i\end{pmatrix}a^{i}b^{n-i}[/tex]
     
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