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Math Help - Integral

  1. #1
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    Integral

    Hello


    How do you integrate this, Integral (5x/3)*e^-x/3


    Thank you
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  2. #2
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    Hello,

    Quote Originally Posted by mladen View Post
    Hello


    How do you integrate this, Integral (5x/3)*e^-x/3


    Thank you
    When you have the integral of a product involving a polynomial (5x/3) and a "basic" exponential (e^-x/3), think "Integration by parts".

    Take u'(x)=\text{exponential thing} and v(x)=\text{polynomial thing}
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  3. #3
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    You refer to partiall integration?


    F(x)g(x) - integral F(x)g(x)´


    Så I should set F(x) = 5x/3 and g(x) = e^-x/3 ?

    thank you
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  4. #4
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    Quote Originally Posted by mladen View Post
    You refer to partiall integration?


    F(x)g(x) - integral F(x)g(x)´


    Så I should set F(x) = 5x/3 and g(x) = e^-x/3 ?

    thank you
    Hm...

    This is not the formula, but it looks like...

    \int_a^b f(x)g'(x) dx=\left[f(x)g(x)\right]_a^b - \int_a^b f'(x)g(x) dx

    And take f(x)=5x/3 and g'(x)=e^{-x/3}






    Edit : your writing is confusing me... What is the original integral with f and g for you ?
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  5. #5
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    The original integral is "integral 5x/3*e^-x/3"


    I set g(x) = e^-x/3
    And f(x) = 5x/3


    then used the formula

    F(x)g(x) - integral F(x)g(x)´
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  6. #6
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    Quote Originally Posted by mladen View Post
    The original integral is "integral 5x/3*e^-x/3"


    I set g(x) = e^-x/3
    And f(x) = 5x/3


    then used the formula

    F(x)g(x) - integral F(x)g(x)´
    Ok that's it

    Set f(x)=e^-x/3
    And g(x)=5x/3

    Because g will be differentiated. Since the derivative of an exponential is in most case the same, it's not really useful to set g(x)=e^-x/3
    Whereas if you differentiate a polynomial (5x/3), you will soon get to a constant.
    Do you understand ?

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  7. #7
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    Yes I think I understand it now. Thanks alot =)
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