What is the integral from 0 to infinity of xe^{-bx} ?

The integral from 0 to infinity of xe^{-bx} is 1/(b^2)

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integral from 0 to infinity of xe^{-bx}

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

\frac{1}{b ^{2}}

Solution steps

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

Compute the indefinite integral:

\int x e^{- b x} d x = \frac{1}{b ^{2}} (- b e^{- b x} x - e^{- b x}) + C

Compute the boundaries:

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

= 0 - (- \frac{1}{b ^{2}})

Simplify

= \frac{1}{b ^{2}}

y = \frac{x}{x + 6}, (4, 0.2)

\int x^{2} (x^{3} - 11)^{6} d x

n = 1 \sum \infty \frac{1}{1 + 2 ^{n}}

ln (1 + x^{5})

\int x^{2} 11 + x^{3} d x

What is the integral from 0 to infinity of xe^{-bx} ?
The integral from 0 to infinity of xe^{-bx} is 1/(b^2)