What is the integral from-infinity to 0 of xe^{9x} ?

The integral from-infinity to 0 of xe^{9x} is -1/81

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integral from-infinity to 0 of xe^{9x}

\int_{- \infty}^{0} x e^{9 x} d x

- \frac{1}{81}

Decimal

- 0.01234 \dots

Solution steps

\int_{- \infty}^{0} x e^{9 x} d x

Compute the indefinite integral:

\int x e^{9 x} d x = \frac{1}{81} (e^{9 x} \cdot 9 x - e^{9 x}) + C

Compute the boundaries:

\int_{- \infty}^{0} x e^{9 x} d x = - \frac{1}{81} - 0

= - \frac{1}{81} - 0

Simplify

= - \frac{1}{81}

What is the integral from-infinity to 0 of xe^{9x} ?
The integral from-infinity to 0 of xe^{9x} is -1/81