What is the integral of 1/9 x^{-2/9} ?

The integral of 1/9 x^{-2/9} is 1/7 x^{7/9}+C

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

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

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

Solution steps

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

Take the constant out:

\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

Apply the Power Rule

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

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

Simplify

\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}}

Add a constant to the solution

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

\frac{\partial}{\partial x} (y^{2} \cdot x)

\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})

What is the integral of 1/9 x^{-2/9} ?
The integral of 1/9 x^{-2/9} is 1/7 x^{7/9}+C