integral of 1/3 x^{(-2)/3}

解答

\int \frac{1}{3} x^{\frac{- 2}{3}} d x

x^{\frac{1}{3}} + C

求解步骤

\int \frac{1}{3} x^{\frac{- 2}{3}} d x

提出常数:

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

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

使用幂法则

= \frac{1}{3} \cdot 3 x^{\frac{1}{3}}

化简

\frac{1}{3} \cdot 3 x^{\frac{1}{3}} : x^{\frac{1}{3}}

= x^{\frac{1}{3}}

解答补常数

= x^{\frac{1}{3}} + C

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