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Math Help - Integration

  1. #1
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    Integration

    Is it possible to integrate (t^2e^-t)/(t + 1)??
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  2. #2
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    yes,,you can use quotient rule...
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  3. #3
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    Isn't quotient rule for differentiation??
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    Quote Originally Posted by CookieC View Post
    Isn't quotient rule for differentiation??
     \int t^2 e^{-t} (t+1)^{-1}

     \int t^2 e^{-(t+1) + 1} (t+1)^{-1}

     e \int t^2 e^{-(t+1) } (t+1)^{-1}

    Let  u = t + 1

     e \int (u-1)^2 e^{-u } (u)^{-1}

     e \int \frac{ u^2 - 2u + 1 }{ ue^u }

     e \int \frac{ u}{ e^u } - 2e \int e^{-u} + e \int (ue^u)^{-1}

    All of the above can be evaluated fairly easily. Use By Parts for most of them.
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  5. #5
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    (ue^u)-1

    uumm how do you integrate that one??
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  6. #6
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    Quote Originally Posted by CookieC View Post
    (ue^u)-1

    uumm how do you integrate that one??
    I lied, we cannot use by parts on that particular integral. It cannot be evaluated in elementary functions: Wolfram Mathematica Online Integrator

    It's defined as  Ei(-x)

    So it would appear as if I have taken you down a path where you can integrate the integrand but not in terms of elementary functions. I'm sure an alternative approach will yield a result that can be fully explained in terms of elementary functions (i'll think of another way to start it off).

    Calling...Simplependulum!!
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  7. #7
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    Quote Originally Posted by CookieC View Post
    Is it possible to integrate (t^2e^-t)/(t + 1)??
    Where has this integral come from? Is it meant to be indefinite or defininte?
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  8. #8
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    Its an indefinite integral..got it from my tutorial sheet...
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  9. #9
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    Quote Originally Posted by CookieC View Post
    Its an indefinite integral..got it from my tutorial sheet...
    Are you expected to solve it using elementary functions?
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  10. #10
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    That's where the problem lies we're suppose to solve it using elementary functions but I've searched it and apparently it cant be done using elementary >.< Might go back and ask the tutor whether the question is right...
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