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

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

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integral from-infinity to 0 of xe^{(3x)}

\int_{- \infty}^{0} x e^{(3 x)} d x

- \frac{1}{9}

Decimal

- 0.11111 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= - \frac{1}{9} - 0

Simplify

= - \frac{1}{9}

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