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

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

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

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

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

Solution steps

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

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

Add a constant to the solution

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

\int e^{2 x} - x^{2} - 1 d x

\frac{d}{d x} (cos (2 x))

y^{^{'}} = y (x y^{2} + 1)

\int 4 sin^{6} (x) cos^{3} (x) d x

(y + x^{2} - y^{2}) d x - x d y = 0

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