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Math Help - laplace transform with powers of t*exponential

  1. #1
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    laplace transform with powers of t*exponential

    Hi all,
    I have a question.

    f(t) =t^3*e^-4t using theorm 1 and 2.

    what im wondering is can I take the t^3 outside the integral as a constant


    t^3| e^-st * e^-4t (between 0 and infinity)

    then

    t^3 [ e-st/-s + e^-4t/s] (between 0 and infinity) or should I be thinking of partial fractions all of which are kind of new to me.
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  2. #2
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    Re: laplace transform with powers of t*exponential

    by the way I need to show all steps rather than refering to the tables, according to which I should end up with


    6/s^4 * 4/s+4
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  3. #3
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    Re: laplace transform with powers of t*exponential

    Quote Originally Posted by tolka View Post
    Hi all,
    I have a question.

    f(t) =t^3*e^-4t using theorm 1 and 2.

    what im wondering is can I take the t^3 outside the integral as a constant
    No, you can't, because it is NOT a constant. The Lalace transform is, by definition
    \int_0^\infty f(t)e^{-st}dt= \int_0^\infty  t^3e^{-4t}e^{-st}dt= \int_0^\infty t^3e^{(-4-s)t}dt
    Do that "by parts" three times.


    t^3| e^-st * e^-4t (between 0 and infinity)

    then

    t^3 [ e-st/-s + e^-4t/s] (between 0 and infinity) or should I be thinking of partial fractions all of which are kind of new to me.
    Thanks from tolka
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  4. #4
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    Re: laplace transform with powers of t*exponential

    Do you mean partial fractions or int by parts?
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