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Integration By Substitution Problem (Trig)

  1. May 20, 2013 #1
    1. The problem statement, all variables and given/known data

    Integrate the following using substitution techniques

    ∫e3tcsc(e3t)cot(e3t) dt

    2. Relevant equations

    csc(t) = 1/sin(t)

    cot(t) = 1/tan(t)

    cot(t) = cos(t)/sin(t)

    1 + cot2(t) = csc2(t)

    3. The attempt at a solution

    ∫e3tcsc(e3t)cot(e3t) dt

    set u = cot(e3t)

    du = (3e3t)(- csc2(e3t)) dt

    Make Substitution,

    ∫e3tcsc(e3t) (u) (1/(3e3t)(- csc2(e3t)) du

    Whoops, csc does not cancel out..

    My friend told me I had to make TWO substitutions, following this advice my head proceeded to explode.

    After recollecting the pieces of my skull fragments and carefully gluing them together again, I posted this question.
  2. jcsd
  3. May 20, 2013 #2


    Staff: Mentor

    I would be inclined to turn the cot and csc functions into their sine and cosine equivalents, and go from there.
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