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受欢迎的微积分 >

integral from 1 to 2 of (e^{1/(x^5)})/(x^6)

解答

\int_{1}^{2} \frac{e ^{\frac{1}{x ^{5}}}}{x ^{6}} d x

解答

\frac{e - 32 e}{5}

+1

十进制

0.33730 \dots

求解步骤

\int_{1}^{2} \frac{e ^{\frac{1}{x ^{5}}}}{x ^{6}} d x

使用换元积分法

= \int_{1}^{32} \frac{e ^{\frac{1}{u}}}{5 u ^{2}} 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_{1}^{32} \frac{e ^{\frac{1}{u}}}{u ^{2}} d u

使用换元积分法

= \frac{1}{5} \cdot \int_{1}^{\frac{1}{32}} - e^{v} d v

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= \frac{1}{5} (- \int_{\frac{1}{32}}^{1} - e^{v} d v)

提出常数:

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

= \frac{1}{5} (- (- \int_{\frac{1}{32}}^{1} e^{v} d v))

使用积分常见定则:

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

= \frac{1}{5} (- (- [e^{v}]_{\frac{1}{32}}^{1}))

化简

= \frac{1}{5} [e^{v}]_{\frac{1}{32}}^{1}

带入上下限计算后得:

e - 32 e

= \frac{1}{5} (e - 32 e)

化简

= \frac{e - 32 e}{5}

作图

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(2dy)/(dx)+10y=5

\frac{2 d y}{d x} + 10 y = 5