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Math Help - Which rule of integration applies here?

  1. #1
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    Which rule of integration applies here?

    I need to integrate (x^4)(e^-x) but am not sure what rule it is.

    Thanks.
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Which rule of integration applies here?

    Have you tried integration by parts?
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  3. #3
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    Re: Which rule of integration applies here?

    Quote Originally Posted by Siron View Post
    Have you tried integration by parts?
    See I thought it was obviously this but then it didn't work out, unless I made a momentous miscalculation somewhere.

    EDIT: Oh no wait by parts does work, it just takes a lot of workings.
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Which rule of integration applies here?

    Can you show some work? Proably you'll need integration by parts 4 times.
    We have:
    \int x^4e^{-x}dx=\int x^4d(-e^{-x})=-x^4e^{-x}+\int e^{-x}4x^3dx=-x^4e^{-x}+4\int e^{-x}x^3dx

    Now you have to apply integration by parts again to calculate:
    \int e^{-x}x^3dx

    etc ...
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  5. #5
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    Re: Which rule of integration applies here?

    Quote Originally Posted by Siron View Post
    Can you show some work? Proably you'll need integration by parts 4 times.
    We have:
    \int x^4e^{-x}dx=\int x^4d(-e^{-x})=-x^4e^{-x}+\int e^{-x}4x^3dx

    Now you have to apply integration by parts again to calculate:
    \int e^{-x}x^3dx

    etc ...
    Thanks for your time, I just reworked it and got the correct answer, I must have gone wrong somewhere.
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Which rule of integration applies here?

    You're welcome
    In fact it's not difficult, you just have to pay attention with the signs etc ...
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  7. #7
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    Re: Which rule of integration applies here?

    Quote Originally Posted by Siron View Post
    You're welcome
    In fact it's not difficult, you just have to pay attention with the signs etc ...
    Yeah it's easy, I have a habit of working too fast when patience is required. :P
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