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受欢迎的微积分 >

integral from 0 to ln(5) of 2e^{3x}

解答

\int_{0}^{l n (5)} 2 e^{3 x} d x

解答

\frac{248}{3}

+1

十进制

82.66666 \dots

求解步骤

\int_{0}^{l n (5)} 2 e^{3 x} d x

提出常数:

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

= 2 \cdot \int_{0}^{l n (5)} e^{3 x} d x

使用换元积分法

= 2 \cdot \int_{0}^{3 l n (5)} e^{u} \frac{1}{3} d u

提出常数:

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

= 2 \cdot \frac{1}{3} \cdot \int_{0}^{3 l n (5)} e^{u} d u

使用积分常见定则:

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

= 2 \cdot \frac{1}{3} [e^{u}]_{0}^{3 l n (5)}

化简

2 \cdot \frac{1}{3} [e^{u}]_{0}^{3 l n (5)} : \frac{2}{3} [e^{u}]_{0}^{3 l n (5)}

= \frac{2}{3} [e^{u}]_{0}^{3 l n (5)}

带入上下限计算后得:

124

= \frac{2}{3} \cdot 124

化简

= \frac{248}{3}

作图

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