What is the integral of (e^y)/((e^y+1)^3) ?

The integral of (e^y)/((e^y+1)^3) is -1/(2(e^y+1)^2)+C

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integral of (e^y)/((e^y+1)^3)

\int \frac{e ^{y}}{( e ^{y} + 1 ) ^{3}} d y

- \frac{1}{2 ( e ^{y} + 1 ) ^{2}} + C

Solution steps

\int \frac{e ^{y}}{( e ^{y} + 1 ) ^{3}} d y

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2 u ^{2}}

Substitute back

u = e^{y} + 1

= - \frac{1}{2 ( e ^{y} + 1 ) ^{2}}

Add a constant to the solution

= - \frac{1}{2 ( e ^{y} + 1 ) ^{2}} + C

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What is the integral of (e^y)/((e^y+1)^3) ?
The integral of (e^y)/((e^y+1)^3) is -1/(2(e^y+1)^2)+C