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

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

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

\frac{1}{3}

Decimal

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}

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