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

The integral from 1 to infinity of xe^{1-x} is 2

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integral from 1 to infinity of xe^{1-x}

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

2

Solution steps

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

Compute the indefinite integral:

\int x e^{1 - x} d x = - e^{1 - x} x - e^{1 - x} + C

Compute the boundaries:

\int_{1}^{\infty} x e^{1 - x} d x = 0 - (- 2)

= 0 - (- 2)

Simplify

= 2

\int_{2}^{11} x d x

\int_{1}^{2} (\frac{9}{x} - e^{- x}) d x

\int_{2}^{3} 95 + 972 x^{2} - 18 x d x

\int_{0}^{20} 2 x d x

\int_{0}^{4} \frac{1}{49 x ^{2} + 81} d x

What is the integral from 1 to infinity of xe^{1-x} ?
The integral from 1 to infinity of xe^{1-x} is 2