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Math Help - Integrating Factor

  1. #1
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    Integrating Factor

    I don't get the step in the red box.

    But.. here's what I have:
    <br />
I = e^{ \int \frac{x}{x^2 + 5} \, dx}

    I = e^{\int x \frac{1}{x^2 + 5} \, dx}

    I = e^{\frac{1}{2}x^2 + ln(x^2 + 5)}

    I = e^{\frac{1}{2}x^2}e^{ln(x^2 + 5)}

    I = e^{x}(x^2 + 5)
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  2. #2
    Moo
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    Hi,

    Substitute t=x^2+5, it should help you see the red step.

    and what you did is wrong o.O \int fg \neq \int f \int g
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  3. #3
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    Quote Originally Posted by Moo View Post
    Hi,

    Substitute t=x^2+5, it should help you see the red step.

    and what you did is wrong o.O \int fg \neq \int f \int g
    I did that but I still don't know what to do...

    u = x^2 + 5

    du = 2x + 5 \, dx

    I = e^{\int (x)(\frac{1}{u}(\frac{1}{2x + 5}) \, du}

    How do I cancel the "x"s if there's an addition at the denominator ??
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  4. #4
    Moo
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    Quote Originally Posted by Macleef View Post
    I did that but I still don't know what to do...

    u = x^2 + 5

    du = 2x + 5 \, dx

    I = e^{\int (x)(\frac{1}{u}(\frac{1}{2x + 5}) \, du}

    How do I cancel the "x"s if there's an addition at the denominator ??
    What is the derivative of x^2+5 with respect to x ??
    What is the derivative of a constant ?

    du is not (2x+5) dx.

    I'm sorry, I'll let you search for your mistake, I won't tell you the solution
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    wow... I've been doing so much differentiation that I almost forgot all basic rules of derivatives. Thank you!
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  6. #6
    Moo
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    Quote Originally Posted by Macleef View Post
    wow... I've been doing so much differentiation that I almost forgot all basic rules of derivatives. Thank you!
    That's less scary !
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