What is the integral of 3/2 xe^{-6x} ?

The integral of 3/2 xe^{-6x} is 1/24 (-6e^{-6x}x-e^{-6x})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3/2 xe^{-6x}

\int \frac{3}{2} x e^{- 6 x} d x

\frac{1}{24} (- 6 e^{- 6 x} x - e^{- 6 x}) + C

Solution steps

\int \frac{3}{2} x e^{- 6 x} d x

Take the constant out:

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

= \frac{3}{2} \cdot \int x e^{- 6 x} d x

Apply u-substitution

: \int \frac{e ^{u} u}{36} d u

= \frac{3}{2} \cdot \int \frac{e ^{u} u}{36} d u

Take the constant out:

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

= \frac{3}{2} \cdot \frac{1}{36} \cdot \int e^{u} u d u

Apply Integration By Parts

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

= \frac{3}{2} \cdot \frac{1}{36} (e^{u} u - \int e^{u} d u)

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

= \frac{3}{2} \cdot \frac{1}{36} (e^{u} u - e^{u})

Substitute back

u = - 6 x

= \frac{3}{2} \cdot \frac{1}{36} (e^{- 6 x} (- 6 x) - e^{- 6 x})

Simplify

\frac{3}{2} \cdot \frac{1}{36} (e^{- 6 x} (- 6 x) - e^{- 6 x}) : \frac{1}{24} (- 6 e^{- 6 x} x - e^{- 6 x})

= \frac{1}{24} (- 6 e^{- 6 x} x - e^{- 6 x})

Add a constant to the solution

= \frac{1}{24} (- 6 e^{- 6 x} x - e^{- 6 x}) + C

6 + \frac{1}{5} sin (6 π t)

x \to 0 lim ((1 + 3 x)^{\frac{2}{x}})

\int \frac{x ^{3}}{x ^{2} + 144} d x

\frac{\partial}{\partial x} (ln (2 x^{2}))

\frac{d}{d x} (\frac{( x ^{3} )}{3})

What is the integral of 3/2 xe^{-6x} ?
The integral of 3/2 xe^{-6x} is 1/24 (-6e^{-6x}x-e^{-6x})+C