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

解答

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

- \frac{1}{9}

十进制

- 0.11111 \dots

求解步骤

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

计算不定积分:

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

带入上下限计算后得:

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

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

化简

= - \frac{1}{9}

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