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5 July, 15:24

How do I find this? ∫ ((e^x) / (2+e^x)) dx

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  1. 5 July, 16:37
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    Use u-substitution where u = 2+e^x

    and since the derivative of e^x is e^x,

    du = e^x

    so in terms of 'u' the integral is

    ∫ (1/u) du (since the contents of u are on the bottom and the contents of du are on top)

    and the integral of 1/u = ln (u) + C, so put x back into the equation using u's value

    ln (u) + C = ln (2+e^x) + C

    (C doesn't change because it just represents an unknown constant)
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