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受欢迎的微积分 >

integral of 1/((1-0.04x)^{0.3)}

解答

\int \frac{1}{( 1 - 0.04 x ) ^{0.3}} d x

解答

- 35.71428 \dots (1 - 0.04 x)^{0.7} + C

求解步骤

\int \frac{1}{( 1 - 0.04 x ) ^{0.3}} d x

使用换元积分法

= \int - \frac{1}{0.04 u ^{0.3}} d u

提出常数:

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

= - \frac{1}{0.04} \cdot \int \frac{1}{u ^{0.3}} d u

化简

= - 25 \cdot \int \frac{1}{u ^{0.3}} d u

使用幂法则

= - 25 \cdot 1.42857 \dots u^{0.7}

u = 1 - 0.04 x

代回

= - 25 \cdot 1.42857 \dots (1 - 0.04 x)^{0.7}

化简

= - 35.71428 \dots (1 - 0.04 x)^{0.7}

解答补常数

= - 35.71428 \dots (1 - 0.04 x)^{0.7} + C

作图

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