What is the integral of e^{-5}x ?

The integral of e^{-5}x is (x^2)/(2e^5)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-5}x

integral

e^{- 5} x

\frac{x ^{2}}{2 e ^{5}} + C

Solution steps

\int e^{- 5} x d x

Take the constant out:

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

= e^{- 5} \cdot \int x d x

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{5}} \cdot \int x d x

Apply the Power Rule

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

= \frac{1}{e ^{5}} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{e ^{5}} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{2 e ^{5}}

= \frac{x ^{2}}{2 e ^{5}}

Add a constant to the solution

= \frac{x ^{2}}{2 e ^{5}} + C

x^{\frac{- 1}{2}}

x^{2} 1 + 4 x^{2}

\frac{1}{( x ( x ^{2} + 1 ) ^{2} )}

5 + x

(sin (x))^{2}