What is the integral of (e^x)/((3-e^x)^2) ?

The integral of (e^x)/((3-e^x)^2) is 1/(3-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)/((3-e^x)^2)

\int \frac{e ^{x}}{( 3 - e ^{x} ) ^{2}} d x

\frac{1}{3 - e ^{x}} + C

Solution steps

\int \frac{e ^{x}}{( 3 - 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 = 3 - e^{x}

= - (- \frac{1}{3 - e ^{x}})

Simplify

= \frac{1}{3 - e ^{x}}

Add a constant to the solution

= \frac{1}{3 - e ^{x}} + C

\int 5 x cos (π x) d x

\int - sin (x) + 3 cos (x) - \frac{1}{x} d x

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

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

\int 400 e^{- 0.1 x} + 8 d x

What is the integral of (e^x)/((3-e^x)^2) ?
The integral of (e^x)/((3-e^x)^2) is 1/(3-e^x)+C