What is the integral from 0 to infinity of u^2e^{-u} ?

The integral from 0 to infinity of u^2e^{-u} is 2

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integral from 0 to infinity of u^2e^{-u}

\int_{0}^{\infty} u^{2} e^{- u} d u

2

Solution steps

\int_{0}^{\infty} u^{2} e^{- u} d u

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} u^{2} e^{- u} d u = 0 - (- 2)

= 0 - (- 2)

Simplify

= 2

\frac{\partial}{\partial y} (z - x^{2} + y^{2})

\int 5 x^{2} + 3 d x

- 3 e^{x^{5}}

\frac{\partial}{\partial x} (\frac{5 y}{x ^{2} + y ^{2}})

\int \frac{( x - 1 )}{( x + 1 )} d x

What is the integral from 0 to infinity of u^2e^{-u} ?
The integral from 0 to infinity of u^2e^{-u} is 2