What is the integral from-infinity to 18 of xe^{x/9} ?

The integral from-infinity to 18 of xe^{x/9} is 81e^2

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integral from-infinity to 18 of xe^{x/9}

\int_{- \infty}^{18} x e^{\frac{x}{9}} d x

81 e^{2}

Decimal

598.51354 \dots

Solution steps

\int_{- \infty}^{18} x e^{\frac{x}{9}} d x

Compute the indefinite integral:

\int x e^{\frac{x}{9}} d x = 9 e^{\frac{x}{9}} x - 81 e^{\frac{x}{9}} + C

Compute the boundaries:

\int_{- \infty}^{18} x e^{\frac{x}{9}} d x = 81 e^{2} - 0

= 81 e^{2} - 0

Simplify

= 81 e^{2}

\frac{d}{d x} ((x^{2} - 10 x + 9) 25 - x^{2})

\int (x cos^{2} (y) - sin (y)) d x

\int [cos (\frac{x}{2}) - sin (3 \frac{x}{2})] d x

\frac{d}{d x} (\frac{7}{x ^{- 2}} + \frac{5}{x ^{- 3}})

x, \frac{1}{3} x, x = 25

What is the integral from-infinity to 18 of xe^{x/9} ?
The integral from-infinity to 18 of xe^{x/9} is 81e^2