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Math Help - Integration using reduction formula.

  1. #1
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    Integration using reduction formula.

    I do not understand the concept of reduction formula's at all.

    How would I use a reduction formula to solve the following

    \int{x^4e^x}

    Is there something general to solve any kind of integral of this form.
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  2. #2
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    Quote Originally Posted by gammaman View Post
    I do not understand the concept of reduction formula's at all.

    How would I use a reduction formula to solve the following

    \int{x^4e^x}

    Is there something general to solve any kind of integral of this form.
    The reduction formula for this one is

     <br />
\int x^n e^x\,dx = x^n e^x - n\int x^{n-1} e^x\,dx<br />

    so putting n = 4 gives

     <br />
\int x^4 e^x\,dx = x^4 e^x - 4\int x^{3} e^x\,dx<br />

    now use the formula for n=3

     <br />
\int x^4 e^x\,dx = x^4 e^x - 4\left(x^3 e^x - 3\int x^{2} e^x\,dx\right)<br />

    and keep going until you reach an integral like \int e^x\,dx which you can do.
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