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I need help with finding the intergral of (x^n)(e^x)

  1. Jan 23, 2007 #1
    I need help with finding the intergral of (x^n)(e^x). I already did for 1,2 and 3. I found out that x^n*e^x times the intergral of (x^n-1)e^x. Is there anyway I can genralize for all n s with out having an integral.
     
  2. jcsd
  3. Jan 23, 2007 #2
    Post this in the homework section "Calculus and Beyond" and you are much more likely to get an answer.
     
  4. Jan 24, 2007 #3
    Easy, use integration by part, show the following relationship
    [tex] \int x^n e^x dx = x^ne^x -n\int x^{n-1}e^x dx [/tex]

    Then use the recurrence relation on [tex] \int x^{n-1} e^x dx [/tex].
    You will get
    [tex] \int x^{n} e^x} dx = \sum _{i=0} ^{n} (-1)^i\frac{n!}{(n-i)!}e^xx^{n-i} [/tex]
     
    Last edited: Jan 24, 2007
  5. Jan 24, 2007 #4

    Gib Z

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    Homework Helper

    chanvincent is correct. when its the same integral with e^NEGATIVE x, its a nice definiton for the gamma function.
     
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