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Math Help - e^x integral

  1. #1
    Member akhayoon's Avatar
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    e^x integral

    \int\frac{e^{3x}}{e^x+e^{-x}}

    can you do this with substitution somehow?
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    \int {\frac{{e^{3x} }}<br />
{{e^x + e^{ - x} }}\,dx} = \int {\frac{{e^{4x} }}<br />
{{e^{2x} + 1}}\,dx} .

    Now this is routine, substitute u=e^{2x},

    \int {\frac{{e^{3x} }}<br />
{{e^x + e^{ - x} }}\,dx} = \frac{1}<br />
{2}\int {\frac{u}<br />
{{u + 1}}\,du} = \frac{1}<br />
{2}\left( {\int {du} - \int {\frac{1}<br />
{{u + 1}}\,du} } \right).

    From here the rest is quite straightforward.
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