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Math Help - Integration by substitution

  1. #1
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    Integration by substitution

    Hi

    I'm having a little trouble with this. Integrate using substitution, where u=e^{x/2}

    \int\frac{e^{x/2}}{1+e^x}dx

    Thanks
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  2. #2
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    If u=e^{\frac{x}{2}}, then  \frac{\text{d}{u}}{\text{d}x} = \frac{1}{2}e^{\frac{x}{2}}.

    If e^{x} =\left(e^{\frac{x}{2}}\right)^2 and \int\frac{e^{\frac{x}{2}}}{1+e^x}\;\text{d}x = 2\int\frac{e^{\frac{x}{2}}}{2(1+e^x)}\;\text{d}x, can you finish it from here?
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  3. #3
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    I get to there but not sure where to go.

    Thanks
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  4. #4
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    Well, given the information that you have, substitute \frac{\text{d}u}{\text{d}x} and e^x =\left(e^\frac{x}{2}\right)^2=u^2 into the integral, and then "cancel" the \text{d}x.

    Now you have something you know how to integrate.
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