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Math Help - Help with integration

  1. #1
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    Help with integration

    It's the integration of

    [x^(3/2)][e^(-x)] from 0 to infinity

    I tried to do integration by parts, but that didn't work out.

    I know what the answer is but I don't know how to get there.

    Any help would be great

    Thanks
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  2. #2
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    Quote Originally Posted by Chloe18 View Post
    It's the integration of

    [x^(3/2)][e^(-x)] from 0 to infinity

    I tried to do integration by parts, but that didn't work out.

    I know what the answer is but I don't know how to get there.

    Any help would be great

    Thanks

    \int x^{\frac{3}{2}}e^{-x}dx is not elementary, ie, the antiderivative involves functions which are not elementary

    how do you already know the answer?
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  3. #3
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    I have the solution but it's not detailed enough for me to understand it

    I was able to solve the problem until the step i wrote then got stuck.

    It has something to do with kernel of gamma (5/2,1) but i don't know what that means
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  4. #4
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    well if you are willing to use the gamma function, evaluate it at z=5/2


    Gamma function - Wikipedia, the free encyclopedia
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  5. #5
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    [quote=artvandalay11;379292]well if you are willing to use the gamma function, evaluate it at z=5/2

    why is it 5/2 and not 3/2?
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  6. #6
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    [quote=Chloe18;379312]
    Quote Originally Posted by artvandalay11 View Post
    well if you are willing to use the gamma function, evaluate it at z=5/2

    why is it 5/2 and not 3/2?

    You want to evaluate this:
     <br /> <br />
\int_0^\infty x^{\frac{3}{2}}e^{-x}dx<br />


    And the gamma function is this

    \Gamma (z)=\int_0^\infty t^{z-1}e^{-t}dt

    So z-1=\frac{3}{2}

    Now I am not aware of a way to evaluate this for non-integer values, not that I'm an expert with the Gamma function, but it seems to me we're back to using tables and calculators
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  7. #7
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    Oh i get it, thanks


    I looked up the value online
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