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This integral is part of a larger problem I'm working on - I'm stuck (I Think)

Here's the integral:

[tex] = \int -\frac{e^{-x}}{e^{-3x}(1+e^x)}dx[/tex]

I've tried some algebra and substitutions:

[tex] = \int -\frac{e^{2x}}{(1+e^x)}dx[/tex]

[tex] = u=e^x[/tex]

[tex] = du=e^x dx[/tex]

[tex] = \int -\frac{u}{(1+u)}du[/tex]

Is this correct? Is this a standard form for something? - looking like ln()?

OR

could go:

[tex] = \int -\frac{e^{-x}}{e^{-3x}(1+e^x)}dx[/tex]

[tex] = \int -\frac{1}{e^{-2x} +e^{-x}}dx[/tex]

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# Integration Question

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