What is the integral of (e^x)/((7-e^x)^2) ?

The integral of (e^x)/((7-e^x)^2) is 1/(7-e^x)+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)/((7-e^x)^2)

\int \frac{e ^{x}}{( 7 - e ^{x} ) ^{2}} d x

\frac{1}{7 - e ^{x}} + C

Solution steps

\int \frac{e ^{x}}{( 7 - e ^{x} ) ^{2}} d x

Apply u-substitution

: \int - \frac{1}{u ^{2}} d u

= \int - \frac{1}{u ^{2}} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - (- \frac{1}{u})

Substitute back

u = 7 - e^{x}

= - (- \frac{1}{7 - e ^{x}})

Simplify

= \frac{1}{7 - e ^{x}}

Add a constant to the solution

= \frac{1}{7 - e ^{x}} + C

\frac{d}{d x} (\frac{2 csc ( x )}{3 ^{x}})

f (x) = - sin (x)

\int sin (\frac{π x}{12}) d x

\frac{d}{d x} (\frac{5 x ^{3} + 5 x ^{2}}{x})

\frac{\partial}{\partial x} (x^{3} - 3 x + 3 x y^{2})

What is the integral of (e^x)/((7-e^x)^2) ?
The integral of (e^x)/((7-e^x)^2) is 1/(7-e^x)+C