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Integration question with power of n

  1. Oct 24, 2012 #1
    http://www.xtremepapers.com/papers/...S Level/Mathematics (9709)/9709_w11_qp_33.pdf1. The problem statement, all variables and given/known data
    no. 10i
    cant do ii and iii without doing i first


    2. Relevant equations
    tan(x)
    d/dx(tan(x))=sec^2x
    1+tan^2x=sec^2x


    3. The attempt at a solution
    Okay, my terms at first would be u^n+2 +u^n. Then, du/dx = sec^2x, so i get du/1+u^2 = dx.

    In the end i got (u^n+2 +u^n)/1+u^2. From then on im stuck. Or did i do something wrong at first?
     
  2. jcsd
  3. Oct 24, 2012 #2
    You know that u=tan[x] so du=sec2[x]dx.

    Let's rearrange the integral a little bit to show the following:

    ∫tann[x](tan2[x]+1)dx

    Remember that dx=du/sec2[x]. However, we need to find sec2[x] in terms of u. We use the following identity of sec2[x]=tan2+1 to show now that dx=du/(u2+1)

    ∫un(u2+1)/(u2+1)=∫un

    This now becomes a simple integration problem and you should be able to do the rest.
     
  4. Oct 24, 2012 #3
    oh great! didnt realize the numerator can be factorised like that. Thanks.
     
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