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Problems with calculating integrals

  1. Jan 30, 2006 #1
    :!!) :rofl: This question simply says calculate
    Question
    [integral from 0 to t]xe^-xdx

    this is one of the questions from my calculus online course there are no similar examples to this in the given notebookk
    i have taken the first year calculus but forgot somestuff, this was 3 years ago, this is why i really need help!!!
    Hints is fine as long of course they lead me to the solution.
    This is what i thought i can do , rearrange the equation to somthing like x/e^x dx but now what if i use substitution say u= e^x then du= e^xdx
    now the new limits would go like this whwen x= 0 then u= 1 and when the upper limit x=t then u=e^t i think so far so good, i hope someone can confirm the aligibility of this ??!!!
    Then :
    [integral from 0 to t]x/e^xdx
    =[integral from 1 to e^t]x/u[1/e^x]du
    now i dont know what to do:uhh: :uhh:


    Another question:
    is there a specific method for calculation integrals like this????
    [integral from 2 to 3 ] 1/[x-1][x-4]dx
    also [integral from 0 to 3] 1/([9-x^2]^1/2) dx
    Last but not least is there a website anyoone suggests that has examples of such problems???Thank you for the help
     
    Last edited: Jan 30, 2006
  2. jcsd
  3. Jan 30, 2006 #2

    arildno

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    For your first, use integration by parts.
    For your second, use partial fractions decomposition.
    For your third, use the substitution [tex]x=3\sin(u)[/tex]
     
  4. Jan 30, 2006 #3
    Tabular also works for the first one, if you're familiar with this method. It uses by parts, but it's less time consuming.
     
  5. Jan 31, 2006 #4

    HallsofIvy

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    x/e^x= xe^(-x) doesn't it? Looks like a good candidate for integration by parts.
     
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