What is the integral of (e^x)/((e^x+1)^{10)} ?

The integral of (e^x)/((e^x+1)^{10)} is -1/(9(e^x+1)^9)+C

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integral of (e^x)/((e^x+1)^{10)}

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{10}} d x

- \frac{1}{9 ( e ^{x} + 1 ) ^{9}} + C

Solution steps

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{10}} d x

Apply u-substitution

= \int \frac{1}{u ^{10}} d u

Apply the Power Rule

= - \frac{1}{9 u ^{9}}

Substitute back

u = e^{x} + 1

= - \frac{1}{9 ( e ^{x} + 1 ) ^{9}}

Add a constant to the solution

= - \frac{1}{9 ( e ^{x} + 1 ) ^{9}} + C

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What is the integral of (e^x)/((e^x+1)^{10)} ?
The integral of (e^x)/((e^x+1)^{10)} is -1/(9(e^x+1)^9)+C