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Trying Integration by parts

  • Thread starter narutoish
  • Start date
  • #1
25
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Homework Statement


∫((z^3)(e^z ))dz


Homework Equations



I just tried u dv - ∫v du


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.
 

Answers and Replies

  • #2
PeroK
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You just have to keep going. Parts, parts and parts again!
 
  • #3
113
10

Homework Statement


∫((z^3)(e^z ))dz


Homework Equations



I just tried u dv - ∫v du


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.
Integrate [itex] ∫(3e^{z} (z^{2})) dz [/itex] with integration by parts till you get the term[itex] ∫e^{z}dz [/itex]
 
  • #4
Ray Vickson
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Homework Statement


∫((z^3)(e^z ))dz


Homework Equations



I just tried u dv - ∫v du


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.
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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