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Homework Help: Calculus 1 Integration Problem

  1. Aug 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Calc I problem, so need to solve by calc 1 methods.

    ∫ (x-1)(x+1)^11 dx

    2. Relevant equations

    3. The attempt at a solution

    ∫ (x-1)(x+1)^11 dx

    U = x+1
    dU = dx
    x-1 = x+1-2 = U-2

    =∫ (U-2)U^11 dU

    =∫ U^12 dU - 2∫ U^11 dU

    =(1/13)U^13 - (1/6)U^12

    =(1/13)(x+1)^13 - (1/6)(X+1)^12

    ∫ (x-1)(x+1)^11 dx = (1/13)(x+1)^13 - (1/6)(X+1)^12

    The course ended already, this was the final test problem (on the test that ended already). I didn't understand how to do this one. I can check my answer and see it's wrong. My teacher won't be in until fall semester starts, so I can't ask him until then. I was already at full time, so Calc I was basically a free class I retook because it could boost GPA without being time consuming.
    Last edited: Aug 9, 2012
  2. jcsd
  3. Aug 9, 2012 #2
    [tex] \int (x-1)(x+1)^{11} dx \\ = \int x(x+1)^{11}-(x+1)^{11} dx \\ = \int [(x+1)-1](x+1)^{11}-(x+1)^{11} dx \\ = \int (x+1)^{12}-2(x+1)^{11} dx \\ = \frac{(x+1)^{13}}{13}-\frac{(x+1)^{12}}{6} +C[/tex]
  4. Aug 9, 2012 #3
    That seems to be the answer I got. Forgot all those constants on my answers >_<. When I take the derivative of that I get:

    (x+1)^12 - 2(x+1)^11 =/= (x-1)(x+1)^11

    I might be missing something here.
  5. Aug 9, 2012 #4
    But it is, isn't it?

    ##(x+1)^{12} - 2(x+1)^{11}##
    ##(x+1)(x+1)^{11} - 2(x+1)^{11}##
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