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Math Help - Substitution, again...

  1. #1
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    Substitution, again...

    Substitution, again...-math_image.gif

    Please show steps. I'm trying to learn how to do these. I have the answers in the back of the book I just need to know how to get there. Thanks.
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  2. #2
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    Re: Substitution, again...

    Quote Originally Posted by njdurkin View Post
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    Please show steps. I'm trying to learn how to do these. I have the answers in the back of the book I just need to know how to get there. Thanks.
    1. Let u = 2+e^x~\implies~\frac{du}{dx} = e^x~\implies~\boxed{du=e^x \cdot dx}

    2. Re-write the integral:

    \int\left(\frac{e^x}{2+e^x}\right) dx = \int\left(\frac1{2+e^x}\right) e^x \cdot dx

    3. Now replace 2+e^x by u and e^x \cdot dx by du. Your integral becomes now:

    \int\left(\frac1u \right) du

    4. Afterwards re-substitute to get a function wrt x.
    Thanks from njdurkin
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