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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \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}})

Simplify

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

Add a constant to the solution

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

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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