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

解答

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

x^{\frac{2}{3}} + C

求解步骤

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

提出常数:

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

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

使用幂法则

= \frac{2}{3} \cdot \frac{3}{2} x^{\frac{2}{3}}

化简

\frac{2}{3} \cdot \frac{3}{2} x^{\frac{2}{3}} : x^{\frac{2}{3}}

= x^{\frac{2}{3}}

解答补常数

= x^{\frac{2}{3}} + C

v o l u m e ab o u t y = 0, y = ln (x), y = 0, [1, 2]

\frac{d y}{d x} = - 9.81 + 0.00375 y^{2}

l a pl a ce t r an s f or m e^{- 3 t} cos (- t)

\int 5 u^{\frac{3}{2}} d u

\frac{d}{d x} (\frac{2 x - 6}{4 - x})