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Help evaluating another integral

  1. Aug 20, 2008 #1
    1. The problem statement, all variables and given/known data
    ∫e^2θ sin 3θ dθ

    2. Relevant equations

    ∫u dv= uv- ∫v du

    3. The attempt at a solution
    u= e^2θ dv=sin 3θ dθ
    du= 2* e^2θ v=(1/3) * - cos 3 θ

    e^2θ 1/3) * - cos 3 θ - ∫1/3) * - cos 3θ 2* e^2θ dθ

    what now
  2. jcsd
  3. Aug 20, 2008 #2


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    Try another IBP (I think that should work)
  4. Aug 20, 2008 #3
    ∫1/3) * - cos 3θ 2* e^2θ dθ
    u= cos 3θ dv= e^2θ
    du= 3*sin 3θ v= e^2θ
    cos 3θ e^2θ - ∫ e^2θ 3*sin 3θ
    e^2θ 1/3) *(2/3) - cos 3 θ +cos 3θ e^2θ - ∫ e^2θ 3*sin 3θ
  5. Aug 20, 2008 #4


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    Integrate by parts once more. You will obtain another integral that is a multiple of the original one. Combine common terms (all the integrals on the left) and solve.
  6. Aug 20, 2008 #5
    is my v correct for the second igb
  7. Aug 20, 2008 #6
    ibp i mean
  8. Aug 20, 2008 #7


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    I'm having some trouble reading your working. I noticed a single "e^2θ 1/3)" term. You should not have any e^(2θ) without an accompanying cos or sin term. Check your working.
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