What is the integral of (e^x)/((e^x+1)^{13)} ?

The integral of (e^x)/((e^x+1)^{13)} is -1/(12(e^x+1)^{12)}+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)^{13)}

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{13}} d x

- \frac{1}{12 ( e ^{x} + 1 ) ^{12}} + C

Solution steps

\int \frac{e ^{x}}{( e ^{x} + 1 ) ^{13}} d x

Apply u-substitution

: \int \frac{1}{u ^{13}} d u

= \int \frac{1}{u ^{13}} d u

Apply the Power Rule

: - \frac{1}{12 u ^{12}}

= - \frac{1}{12 u ^{12}}

Substitute back

u = e^{x} + 1

= - \frac{1}{12 ( e ^{x} + 1 ) ^{12}}

Add a constant to the solution

= - \frac{1}{12 ( e ^{x} + 1 ) ^{12}} + C

\int \frac{3 x ^{b - 1}}{a + x ^{b}} d x

\int ln (x e^{x}) d x

\int \frac{x ^{2}}{1 - 4 x ^{2}} d x

\int 2 x^{3} + \frac{5}{x ^{2}} - \frac{7}{x} d x

\int (12 x^{\frac{3}{4}} - 9 x^{\frac{5}{3}}) d x

What is the integral of (e^x)/((e^x+1)^{13)} ?
The integral of (e^x)/((e^x+1)^{13)} is -1/(12(e^x+1)^{12)}+C