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Trying Integration by parts

  1. Feb 4, 2014 #1
    1. The problem statement, all variables and given/known data
    ∫((z^3)(e^z ))dz

    2. Relevant equations

    I just tried u dv - ∫v du

    3. The attempt at a solution

    u = z^3 dv = e^z
    du = 3z^2 v = e^z

    = z^3e^z - ∫(3e^z (z^2)) dz

    I got this far but after that if I try integration by parts again, it gets too confusing.
  2. jcsd
  3. Feb 4, 2014 #2


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    You just have to keep going. Parts, parts and parts again!
  4. Feb 4, 2014 #3
    Integrate [itex] ∫(3e^{z} (z^{2})) dz [/itex] with integration by parts till you get the term[itex] ∫e^{z}dz [/itex]
  5. Feb 4, 2014 #4

    Ray Vickson

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    You can avoid confusion by using some extra symbols. Let ##I = \int z^3 e^z \, dz##. Integration by parts gives you ##I = z^3 e^z - 3I_1##, where ##I_1 = \int z^2 e^z \, dz##. Now look at ##I_1## in the same way, etc. Using separate symbols like that helps to keep things straight and to reduce errors.
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