What is the integral of (e^x)/((e^x+1)^{11)} ?

The integral of (e^x)/((e^x+1)^{11)} is -1/(10(e^x+1)^{10)}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (e^x)/((e^x+1)^{11)}

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{11}} d x

- \frac{1}{10 ( e ^{x} + 1 ) ^{10}} + C

Solution steps

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{11}} d x

Apply u-substitution

: \int \frac{1}{u ^{11}} d u

= \int \frac{1}{u ^{11}} d u

Apply the Power Rule

: - \frac{1}{10 u ^{10}}

= - \frac{1}{10 u ^{10}}

Substitute back

u = e^{x} + 1

= - \frac{1}{10 ( e ^{x} + 1 ) ^{10}}

Add a constant to the solution

= - \frac{1}{10 ( e ^{x} + 1 ) ^{10}} + C

\int (x^{1.2} + 9 x^{3.5}) d x

\int tan^{3} (x) sec^{\frac{- 1}{2}} (x) d x

\int x^{2} (x^{3} - 8)^{4} d x

\int \frac{- 8 x + 24}{( x ^{2} + 2 x + 4 ) ^{2}} d x

\int x e^{- 1 x} d x

What is the integral of (e^x)/((e^x+1)^{11)} ?
The integral of (e^x)/((e^x+1)^{11)} is -1/(10(e^x+1)^{10)}+C