What is the integral from 0 to 1 of x*e^{-x} ?

The integral from 0 to 1 of x*e^{-x} is -2/e+1

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integral from 0 to 1 of x*e^{-x}

\int_{0}^{1} x \cdot e^{- x} d x

- \frac{2}{e} + 1

Decimal Notation

0.26424 \dots

Solution steps

\int_{0}^{1} x e^{- x} d x

Apply Integration By Parts

: [- e^{- x} x - \int - e^{- x} d x]_{0}^{1}

= [- e^{- x} x - \int - e^{- x} d x]_{0}^{1}

\int - e^{- x} d x = e^{- x}

= [- e^{- x} x - e^{- x}]_{0}^{1}

Compute the boundaries:

- \frac{2}{e} + 1

= - \frac{2}{e} + 1

\int_{0}^{1} (e^{- x}) d x

f (x) = x^{2} (1 - 9 x)

\int sin (3 x) cos (5 x) d x

(3 x^{2} y - 6 x) d x + (x^{3} + 2 y) d y = 0

\int_{4}^{6} \frac{1}{x ^{2} - 1} d x

What is the integral from 0 to 1 of x*e^{-x} ?
The integral from 0 to 1 of x*e^{-x} is -2/e+1