What is the integral from-infinity to 0 of xe^{6x} ?

The integral from-infinity to 0 of xe^{6x} is -1/36

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integral from-infinity to 0 of xe^{6x}

\int_{- \infty}^{0} x e^{6 x} d x

- \frac{1}{36}

Decimal

- 0.02777 \dots

Solution steps

\int_{- \infty}^{0} x e^{6 x} d x

Compute the indefinite integral:

\int x e^{6 x} d x = \frac{1}{36} (e^{6 x} \cdot 6 x - e^{6 x}) + C

Compute the boundaries:

\int_{- \infty}^{0} x e^{6 x} d x = - \frac{1}{36} - 0

= - \frac{1}{36} - 0

Simplify

= - \frac{1}{36}

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What is the integral from-infinity to 0 of xe^{6x} ?
The integral from-infinity to 0 of xe^{6x} is -1/36