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U substitution with trig

  1. Feb 13, 2012 #1

    jtt

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    1. The problem statement, all variables and given/known data
    use substitution to evaluate the integral


    2. Relevant equations
    1)∫ tan(4x+2)dx
    2)∫3(sin x)^-2 dx

    3. The attempt at a solution
    1) u= 4x+2 du= 4
    (1/4)∫4 tan(4x+2) dx
    ∫(1/4)tan(4x+2)(4dx)
    ∫ (1/4) tanu du
    (1/4)ln ltan(u)l +c

    2) u=sinx du= cosx or u=x du = 1 ????
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 13, 2012 #2
    For your first integral, you evaluated ∫tan(u)du incorrectly.
    ∫tan(u) du = ∫sin(u)/cos(u) du
    = -∫-sin(u)/cos(u) du
    So now solve for this integral, given that ∫f'(x)/f(x) dx = ln(|f(x)|) + c

    For your second, I'm not sure why you would use 'u' substitution,
    because 1/sin^2(x) = csc^2(x), which has the integral of -cot(x) + c.

    I'll leave that to you to find a way with u-substitution.
     
    Last edited: Feb 13, 2012
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