What is the integral of xe^{-3} ?

The integral of xe^{-3} is (x^2)/(2e^3)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of xe^{-3}

\int x e^{- 3} d x

\frac{x ^{2}}{2 e ^{3}} + C

Solution steps

\int x e^{- 3} d x

Take the constant out:

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

= e^{- 3} \cdot \int x d x

Apply exponent rule:

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

= \frac{1}{e ^{3}} \cdot \int x d x

Apply the Power Rule

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

= \frac{1}{e ^{3}} \cdot \frac{x ^{2}}{2}

Simplify

\frac{1}{e ^{3}} \cdot \frac{x ^{2}}{2} : \frac{x ^{2}}{2 e ^{3}}

= \frac{x ^{2}}{2 e ^{3}}

Add a constant to the solution

= \frac{x ^{2}}{2 e ^{3}} + C

\int \frac{arctan ( x )}{( 1 + x ^{2} ) ^{2}} d x

\int sin^{4} (\frac{t}{2}) d t

\int sec^{2} (x - 1) d x

\int (\frac{1}{x ^{\frac{3}{2}}} + 1) d x

\int (\frac{x + 2 y}{( x + y ) ^{2}}) d x