What is the integral of (e^x)/((e^x+1)^5) ?

The integral of (e^x)/((e^x+1)^5) is -1/(4(e^x+1)^4)+C

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integral of (e^x)/((e^x+1)^5)

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{5}} d x

- \frac{1}{4 ( e ^{x} + 1 ) ^{4}} + C

Solution steps

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{5}} d x

Apply u-substitution

: \int \frac{1}{( u + 1 ) ^{5}} d u

= \int \frac{1}{( u + 1 ) ^{5}} d u

Apply u-substitution

: \int \frac{1}{v ^{5}} d v

= \int \frac{1}{v ^{5}} d v

Apply the Power Rule

: - \frac{1}{4 v ^{4}}

= - \frac{1}{4 v ^{4}}

Substitute back

= - \frac{1}{4 ( e ^{x} + 1 ) ^{4}}

Add a constant to the solution

= - \frac{1}{4 ( e ^{x} + 1 ) ^{4}} + C

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What is the integral of (e^x)/((e^x+1)^5) ?
The integral of (e^x)/((e^x+1)^5) is -1/(4(e^x+1)^4)+C