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

The integral from 0 to infinity of e^{-x}x^3 is 6

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 e^{-x}x^3

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

6

Solution steps

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

Compute the indefinite integral:

\int e^{- x} x^{3} d x = - e^{- x} x^{3} - 3 (e^{- x} x^{2} - 2 (- e^{- x} x - e^{- x})) + C

Compute the boundaries:

\int_{0}^{\infty} e^{- x} x^{3} d x = 0 - (- 6)

= 0 - (- 6)

Simplify

= 6

\int_{0}^{2 π} - sin (x) cos (x) d x

\int_{0}^{11} 22 x - x^{2} d x

\int_{- 1}^{2} (x + 3) - (x^{2} + 1) d x

\int_{1}^{8} x^{- \frac{10}{3}} d x

\int_{1}^{2} 16 x e^{4 x^{2}} d x

What is the integral from 0 to infinity of e^{-x}x^3 ?
The integral from 0 to infinity of e^{-x}x^3 is 6