What is the integral from-infinity to 0 of xe^{3x+1} ?

The integral from-infinity to 0 of xe^{3x+1} is -e/9

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integral from-infinity to 0 of xe^{3x+1}

\int_{- \infty}^{0} x e^{3 x + 1} d x

- \frac{e}{9}

Decimal Notation

- 0.30203 \dots

Solution steps

\int_{- \infty}^{0} x e^{3 x + 1} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{- \infty}^{0} x e^{3 x + 1} d x = - \frac{e}{9} - 0

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

Simplify

= - \frac{e}{9}

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What is the integral from-infinity to 0 of xe^{3x+1} ?
The integral from-infinity to 0 of xe^{3x+1} is -e/9