1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    User Avatar
    Homework Helper

    chanvincent is correct. when its the same integral with e^NEGATIVE x, its a nice definiton for the gamma function.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook