What is the integral of (4-e^{2x})/(e^{2x)} ?

The integral of (4-e^{2x})/(e^{2x)} is -2e^{-2x}-x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (4-e^{2x})/(e^{2x)}

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

- 2 e^{- 2 x} - x + C

Solution steps

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

Expand

\frac{4 - e ^{2 x}}{e ^{2 x}} : \frac{4}{e ^{2 x}} - 1

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

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{4}{e ^{2 x}} d x = - 2 e^{- 2 x}

\int 1 d x = x

= - 2 e^{- 2 x} - x

Add a constant to the solution

= - 2 e^{- 2 x} - x + C

What is the integral of (4-e^{2x})/(e^{2x)} ?
The integral of (4-e^{2x})/(e^{2x)} is -2e^{-2x}-x+C