What is the integral of 2e^{-2}x ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 2e^{-2}x

integral

2 e^{- 2} x

\frac{x ^{2}}{e ^{2}} + C

Solution steps

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

Take the constant out:

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

= 2 e^{- 2} \cdot \int x d x

2 e^{- 2} = \frac{2}{e ^{2}}

= \frac{2}{e ^{2}} \cdot \int x d x

Apply the Power Rule

= \frac{2}{e ^{2}} \cdot \frac{x ^{2}}{2}

Simplify

\frac{2}{e ^{2}} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{e ^{2}}

= \frac{x ^{2}}{e ^{2}}

Add a constant to the solution

= \frac{x ^{2}}{e ^{2}} + C