What is the integral from 4 to infinity of xe^{-3x} ?

The integral from 4 to infinity of xe^{-3x} is (13)/(9e^{12)}

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integral from 4 to infinity of xe^{-3x}

\int_{4}^{\infty} x e^{- 3 x} d x

\frac{13}{9 e ^{12}}

Decimal

8.87497 E - 6

Solution steps

\int_{4}^{\infty} x e^{- 3 x} d x

Compute the indefinite integral:

\int x e^{- 3 x} d x = \frac{1}{9} (- 3 e^{- 3 x} x - e^{- 3 x}) + C

Compute the boundaries:

\int_{4}^{\infty} x e^{- 3 x} d x = 0 - (- \frac{13}{9 e ^{12}})

= 0 - (- \frac{13}{9 e ^{12}})

Simplify

= \frac{13}{9 e ^{12}}

\frac{d y}{d x} = 2 x y^{2} + 3 x^{2} y^{2}, y (1) = - 1

\int \frac{4 x + 3}{1 - x ^{2}} d x

\frac{d}{d x} (sin (4 x + 7 x^{4}) + e^{1 - x^{2}})

\int \frac{x ^{2} + 24 x - 9}{x ^{3} - 9 x} d x

x \to \frac{π}{2} lim (- cos (x))

What is the integral from 4 to infinity of xe^{-3x} ?
The integral from 4 to infinity of xe^{-3x} is (13)/(9e^{12)}