What is the integral of 1/7 x^{-6/7} ?

The integral of 1/7 x^{-6/7} is x^{1/7}+C

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integral of 1/7 x^{-6/7}

\int \frac{1}{7} x^{- \frac{6}{7}} d x

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

Solution steps

\int \frac{1}{7} x^{- \frac{6}{7}} d x

Take the constant out:

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

= \frac{1}{7} \cdot \int x^{- \frac{6}{7}} d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

y^{2} + x y + x^{2} = 1, (0, 1)

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

\int_{1}^{4} \frac{3}{x} d x

\frac{3}{2 s ^{2} + 3 s + 1}

\frac{d y}{d x} = 2 y e^{x + 7}

What is the integral of 1/7 x^{-6/7} ?
The integral of 1/7 x^{-6/7} is x^{1/7}+C