How do you evaluate the definite integral $\int \frac{e^{x}}{1 + e^{x}}$ $int (e^x)/(1+e^x)$ from $[0, 1]$ $[0,1]$ ?

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Answer 1 · 2016-09-13T07:53:37

$= ln (\frac{1 + e}{2})$ $=ln( (1+e)/2)$

note that $\frac{d}{d x} (ln (1 + e^{x})) = \frac{e^{x}}{1 + e^{x}}$ $d/dx(ln (1+e^x)) = (e^x)/(1+e^x)$

So

$int_0^1 (e^x)/(1+e^x) \ dx$

$=int_0^1 d/dx(ln (1+e^x)) \ dx$

$=[ ln (1+e^x)]_0^1$

$=ln( (1+e)/2)$

How do you evaluate the definite integral int (e^x)/(1+e^x)∫ex1+exint (e^x)/(1+e^x) from [0,1][0,1][0,1]?