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)

integral

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

- \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

\frac{x ^{2}}{( x - 1 )}

x^{2} a^{2} + x^{2}

\frac{sin ^{3} ( x )}{cos ( x )}

sin (5 x + 3)

\frac{x ^{2}}{x ^{2} + 5}

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