integral of 1/9 x^{-2/9}

解答

\int \frac{1}{9} x^{- \frac{2}{9}} d x

\frac{1}{7} x^{\frac{7}{9}} + C

求解步骤

\int \frac{1}{9} x^{- \frac{2}{9}} d x

提出常数:

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

= \frac{1}{9} \cdot \int x^{- \frac{2}{9}} d x

使用幂法则

= \frac{1}{9} \cdot \frac{9}{7} x^{\frac{7}{9}}

化简

\frac{1}{9} \cdot \frac{9}{7} x^{\frac{7}{9}} : \frac{1}{7} x^{\frac{7}{9}}

= \frac{1}{7} x^{\frac{7}{9}}

解答补常数

= \frac{1}{7} x^{\frac{7}{9}} + C

\int_{1}^{9} \frac{1}{2 x ^{2}} d x

x^{2} y^{^{''}} + 2 x y^{^{'}} - 12 y = 0, y (1) = - 1, y^{^{'}} (1) = 10

\frac{d x}{d y} = - \frac{4 y ^{2} + 6 x y}{3 y ^{2} + 2 x}

x \to 2 lim (x^{4})

d er i v a t i v e f (x) = \frac{2}{x - 3}