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

The integral of 3xe^{-3x} is -e^{-3x}x-1/3 e^{-3x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3xe^{-3x}

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

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

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

: \int \frac{e ^{u} u}{9} d u

= 3 \cdot \int \frac{e ^{u} u}{9} d u

Take the constant out:

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

= 3 \cdot \frac{1}{9} \cdot \int e^{u} u d u

Apply Integration By Parts

: e^{u} u - \int e^{u} d u

= 3 \cdot \frac{1}{9} (e^{u} u - \int e^{u} d u)

\int e^{u} d u = e^{u}

= 3 \cdot \frac{1}{9} (e^{u} u - e^{u})

Substitute back

u = - 3 x

= 3 \cdot \frac{1}{9} (e^{- 3 x} (- 3 x) - e^{- 3 x})

Simplify

3 \cdot \frac{1}{9} (e^{- 3 x} (- 3 x) - e^{- 3 x}) : - e^{- 3 x} x - \frac{1}{3} e^{- 3 x}

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

Add a constant to the solution

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

y = x^{2} - 2 x, y = 3 x + 6

\int e^{- x} sin (4 x) d x

(x^{2} + 1) y^{^{'}} + 6 x (y - 1) = 0, y (0) = 8

\int (ln (y))^{2} d y

(x^{2} - 1) (x^{2} - 4), x = 0, x = 5

What is the integral of 3xe^{-3x} ?
The integral of 3xe^{-3x} is -e^{-3x}x-1/3 e^{-3x}+C