What is the integral from-infinity to 0 of 15xe^{3x} ?

The integral from-infinity to 0 of 15xe^{3x} is -5/3

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integral from-infinity to 0 of 15xe^{3x}

\int_{- \infty}^{0} 15 x e^{3 x} d x

- \frac{5}{3}

Decimal

- 1.66666 \dots

Solution steps

\int_{- \infty}^{0} 15 x e^{3 x} d x

Compute the indefinite integral:

\int 15 x e^{3 x} d x = 5 e^{3 x} x - \frac{5}{3} e^{3 x} + C

Compute the boundaries:

\int_{- \infty}^{0} 15 x e^{3 x} d x = - \frac{5}{3} - 0

= - \frac{5}{3} - 0

Simplify

= - \frac{5}{3}

What is the integral from-infinity to 0 of 15xe^{3x} ?
The integral from-infinity to 0 of 15xe^{3x} is -5/3