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Math Help - A tricky integral...

  1. #1
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    A tricky integral...

    Integral of (e^x)/(e^(2x)+3) dx

    U-substitution and integration by parts doesn't seem to be working for me...
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  2. #2
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    There's no much here, just put u=\sqrt3e^x and the remaining integral is an arctangent.
    Last edited by mr fantastic; February 14th 2009 at 06:23 PM.
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  3. #3
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    Can you explain that substitution in a little more detail? I'm not sure how you would use it. Our class isn't going over trigonometric substitutions, but there it is in one of our improper integral problems...
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  4. #4
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    Quote Originally Posted by pianopiano View Post
    Can you explain that substitution in a little more detail? I'm not sure how you would use it. Our class isn't going over trigonometric substitutions, but there it is in one of our improper integral problems...
    Krizalid is not suggesting a trig substitution ....

    Actually, I think the substitution he intended was e^x = \sqrt{3} u \Rightarrow e^{2x} = 3 u^2 and \frac{du}{dx} = \frac{e^x}{\sqrt{3}} \Rightarrow dx = \frac{\sqrt{3}}{e^x} = \frac{\sqrt{3}}{u}.

    So hop to it, make the substitution ....
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  5. #5
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    Ahhh, yes, that's the substitution, my head is in other place.
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