What is the integral from-infinity to 0 of xe^{2+3x} ?

The integral from-infinity to 0 of xe^{2+3x} is -(e^2)/9

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integral from-infinity to 0 of xe^{2+3x}

\int_{- \infty}^{0} x e^{2 + 3 x} d x

- \frac{e ^{2}}{9}

Decimal Notation

- 0.82100 \dots

Solution steps

\int_{- \infty}^{0} x e^{2 + 3 x} d x

Compute the indefinite integral:

\int x e^{2 + 3 x} d x = \frac{1}{3} e^{2 + 3 x} x - \frac{1}{9} e^{2 + 3 x} + C

Compute the boundaries:

\int_{- \infty}^{0} x e^{2 + 3 x} d x = - \frac{e ^{2}}{9} - 0

= - \frac{e ^{2}}{9} - 0

Simplify

= - \frac{e ^{2}}{9}

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What is the integral from-infinity to 0 of xe^{2+3x} ?
The integral from-infinity to 0 of xe^{2+3x} is -(e^2)/9