integral from 2 to 5 of e^{5x}

解答

\int_{2}^{5} e^{5 x} d x

\frac{e ^{25} - e ^{10}}{5}

十进制

14400975462.2

求解步骤

\int_{2}^{5} e^{5 x} d x

使用换元积分法

= \int_{10}^{25} e^{u} \frac{1}{5} d u

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int_{10}^{25} e^{u} d u

使用积分常见定则:

\int e^{u} d u = e^{u}

= \frac{1}{5} [e^{u}]_{10}^{25}

带入上下限计算后得:

e^{25} - e^{10}

= \frac{1}{5} (e^{25} - e^{10})

化简

= \frac{e ^{25} - e ^{10}}{5}

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