What is the integral from 0 to infinity of 3xe^{-3x} ?

The integral from 0 to infinity of 3xe^{-3x} is 1/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to infinity of 3xe^{-3x}

\int_{0}^{\infty} 3 x e^{- 3 x} d x

\frac{1}{3}

Decimal Notation

0.33333 \dots

Solution steps

\int_{0}^{\infty} 3 x e^{- 3 x} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} 3 x e^{- 3 x} d x = 0 - (- \frac{1}{3})

= 0 - (- \frac{1}{3})

Simplify

= \frac{1}{3}

\int \frac{x ^{2} - 1}{x ^{3} - 3 x} d x

\int \frac{x + 6}{x} d x

y = 4 x + 9, (4, 5)

- 4 - 7 x^{2}

y^{^{''}} - 8 y^{^{'}} + 20 = 0

What is the integral from 0 to infinity of 3xe^{-3x} ?
The integral from 0 to infinity of 3xe^{-3x} is 1/3