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})

d er i v a t i v e - 3 e^{x^{5}}

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

\int \frac{2}{25 - 2 x ^{2}} d x

d er i v a t i v e 6 x + \frac{4}{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