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Math Help - Integral problem

  1. #1
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    Integral problem

    Hey,
    In one of my text books that following equation was written:
    Integral problem-untitled.png

    My question is .. Where did the x (In the red circle) go to ? Why is it ignored ?

    Thanks a lot !
    Attached Thumbnails Attached Thumbnails Integral problem-untitled.png  
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  2. #2
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    Re: Integral problem

    Quote Originally Posted by MichaelEngstler View Post
    Hey,
    In one of my text books that following equation was written:
    My question is .. Where did the x (In the red circle) go to ? Why is it ignored ?
    First it was not ignored. It is part of $dt=\dfrac{dx}{x}$.

    Note that the limits of integration also change.
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  3. #3
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    Re: Integral problem

    Can you please explain why dt = dx/x ?
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  4. #4
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    Re: Integral problem

    Quote Originally Posted by MichaelEngstler View Post
    Can you please explain why dt = dx/x ?
    $t = ln(x) \implies \dfrac{dt}{dx} = \dfrac{1}{x} \implies dt = \dfrac{dx}{x}.$
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  5. #5
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    Re: Integral problem

    Quote Originally Posted by MichaelEngstler View Post
    Can you please explain why dt = dx/x ?
    $t=\ln(x)$ so $\dfrac{dt}{dx}=\dfrac{1}{x}$ so $dt=\dfrac{dx}{x}$
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  6. #6
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    Re: Integral problem

    Thanks a lot
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