What is the integral of (e^x)/((1+e^x)^2) ?

The integral of (e^x)/((1+e^x)^2) is -1/(1+e^x)+C

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integral of (e^x)/((1+e^x)^2)

\int \frac{e ^{x}}{( 1 + e ^{x} ) ^{2}} d x

- \frac{1}{1 + e ^{x}} + C

Solution steps

\int \frac{e ^{x}}{( 1 + e ^{x} ) ^{2}} d x

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = 1 + e^{x}

= - \frac{1}{1 + e ^{x}}

Add a constant to the solution

= - \frac{1}{1 + e ^{x}} + C

4 x, 4 x - x^{2}, 0, 2

\frac{d}{d x} (\frac{x ^{3}}{6} + \frac{1}{2 x})

f (x) = - 21 x - 3

y^{^{'}} = 3 + e^{- 5 t}

\frac{d y}{d x} = e^{x - y}, y (ln (3)) = ln (5)

What is the integral of (e^x)/((1+e^x)^2) ?
The integral of (e^x)/((1+e^x)^2) is -1/(1+e^x)+C