What is the integral of (e^x)/((e^x+1)^{18)} ?

The integral of (e^x)/((e^x+1)^{18)} is -1/(17(e^x+1)^{17)}+C

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integral of (e^x)/((e^x+1)^{18)}

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{18}} d x

- \frac{1}{17 ( e ^{x} + 1 ) ^{17}} + C

Solution steps

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{18}} d x

Apply u-substitution

: \int \frac{1}{u ^{18}} d u

= \int \frac{1}{u ^{18}} d u

Apply the Power Rule

: - \frac{1}{17 u ^{17}}

= - \frac{1}{17 u ^{17}}

Substitute back

u = e^{x} + 1

= - \frac{1}{17 ( e ^{x} + 1 ) ^{17}}

Add a constant to the solution

= - \frac{1}{17 ( e ^{x} + 1 ) ^{17}} + C

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What is the integral of (e^x)/((e^x+1)^{18)} ?
The integral of (e^x)/((e^x+1)^{18)} is -1/(17(e^x+1)^{17)}+C