integral from 0 to 5 of xe^{x-5}

解答

\int_{0}^{5} x e^{x - 5} d x

4 + \frac{1}{e ^{5}}

十进制

4.00673 \dots

求解步骤

\int_{0}^{5} x e^{x - 5} d x

使用分布积分法

= [e^{x - 5} x - \int e^{x - 5} d x]_{0}^{5}

\int e^{x - 5} d x = e^{x - 5}

= [e^{x - 5} x - e^{x - 5}]_{0}^{5}

带入上下限计算后得:

4 + \frac{1}{e ^{5}}

= 4 + \frac{1}{e ^{5}}

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