What is the integral of 1/7 x^{-3/7} ?

The integral of 1/7 x^{-3/7} is 1/4 x^{4/7}+C

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integral of 1/7 x^{-3/7}

\int \frac{1}{7} x^{- \frac{3}{7}} d x

\frac{1}{4} x^{\frac{4}{7}} + C

Solution steps

\int \frac{1}{7} x^{- \frac{3}{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{3}{7}} d x

Apply the Power Rule

: \frac{7}{4} x^{\frac{4}{7}}

= \frac{1}{7} \cdot \frac{7}{4} x^{\frac{4}{7}}

Simplify

\frac{1}{7} \cdot \frac{7}{4} x^{\frac{4}{7}} : \frac{1}{4} x^{\frac{4}{7}}

= \frac{1}{4} x^{\frac{4}{7}}

Add a constant to the solution

= \frac{1}{4} x^{\frac{4}{7}} + C

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What is the integral of 1/7 x^{-3/7} ?
The integral of 1/7 x^{-3/7} is 1/4 x^{4/7}+C