What is the integral from-infinity to 12 of xe^{x/3} ?

The integral from-infinity to 12 of xe^{x/3} is 27e^4

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integral from-infinity to 12 of xe^{x/3}

\int_{- \infty}^{12} x e^{\frac{x}{3}} d x

27 e^{4}

Decimal Notation

1474.15005 \dots

Solution steps

\int_{- \infty}^{12} x e^{\frac{x}{3}} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{- \infty}^{12} x e^{\frac{x}{3}} d x = 27 e^{4} - 0

= 27 e^{4} - 0

Simplify

= 27 e^{4}

\int_{- 2}^{2} (x + 7) 4 - x^{2} d x

x \to 0 lim (\frac{csc ( x )}{3 x})

\frac{\partial}{\partial y} (\frac{x}{y} + \frac{y}{z})

\frac{\partial}{\partial z} (x^{2} y + y z^{3} + z^{5} x)

y \to 0 lim (\frac{y ^{2}}{y ^{2}})

What is the integral from-infinity to 12 of xe^{x/3} ?
The integral from-infinity to 12 of xe^{x/3} is 27e^4