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受欢迎的微积分 >

integral of (2-7t)^{2/3}

解答

\int (2 - 7 t)^{\frac{2}{3}} d t

解答

- \frac{3}{35} (2 - 7 t)^{\frac{5}{3}} + C

求解步骤

\int (2 - 7 t)^{\frac{2}{3}} d t

使用换元积分法

= \int - \frac{u ^{\frac{2}{3}}}{7} d u

提出常数:

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

= - \frac{1}{7} \cdot \int u^{\frac{2}{3}} d u

使用幂法则

= - \frac{1}{7} \cdot \frac{3}{5} u^{\frac{5}{3}}

u = 2 - 7 t

代回

= - \frac{1}{7} \cdot \frac{3}{5} (2 - 7 t)^{\frac{5}{3}}

化简

- \frac{1}{7} \cdot \frac{3}{5} (2 - 7 t)^{\frac{5}{3}} : - \frac{3}{35} (2 - 7 t)^{\frac{5}{3}}

= - \frac{3}{35} (2 - 7 t)^{\frac{5}{3}}

解答补常数

= - \frac{3}{35} (2 - 7 t)^{\frac{5}{3}} + C

作图

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