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

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

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

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

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

Solution steps

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

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^{x} + 1

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

Add a constant to the solution

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

y^{^{'}} = ry (1 - \frac{y}{k})

\frac{d}{d x} ((x^{3} - 2)^{5})

x \to 0 lim (x^{14} ln (x))

\frac{d}{d x} (e^{\frac{3}{2} x})

\frac{d}{d x} (\frac{1}{( x - 5 ) ^{2}})

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