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Homework Help: Antiderivatives question

  1. Dec 20, 2009 #1
    1. The problem statement, all variables and given/known data
    1.∫sec^2 (4x+1)dx

    2.∫ root(sin pi theta) cos(pi theta) d(theta)

    3.∫ e^x dx /(1+e^x)

    2. Relevant equations
    1.u=4x+1
    2. u= sin(pi theta)
    3. u= 1+e^x
    antiderivatives to find the answers..
    3. The attempt at a solution
    For #1, tan^4(4x+1)/4 +c..is the answer..but I don't get why tan should be ^4??
    I took the deriv. of the u and replace dx with the stuff that only contains du..not dx...
    And then,,I sometimes have problems solving some questions..
    Please help!
     
  2. jcsd
  3. Dec 20, 2009 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi SAT2400! :smile:

    (have a pi: π and a theta: θ and a square-root: √ and try using the X2 tag just above the Reply box :wink:)
    It's a typo :rolleyes:. tan(4x+1)/4 +c..is the correct answer!
    (You mean ∫ √(sin(πθ)) cos(πθ) dθ ?)

    Those substitutions should be ok (or you could just use u = ex, with the same result) …

    what did you get? :smile:
     
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