What is the integral of 2/4 x^{-8} ?

The integral of 2/4 x^{-8} is -1/(14x^7)+C

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integral of 2/4 x^{-8}

\int \frac{2}{4} x^{- 8} d x

- \frac{1}{14 x ^{7}} + C

Solution steps

\int \frac{2}{4} x^{- 8} d x

Take the constant out:

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

= \frac{2}{4} \cdot \int x^{- 8} d x

Cancel the common factor:

2

= \frac{1}{2} \cdot \int x^{- 8} d x

Apply the Power Rule

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

= \frac{1}{2} (- \frac{1}{7 x ^{7}})

Simplify

\frac{1}{2} (- \frac{1}{7 x ^{7}}) : - \frac{1}{14 x ^{7}}

= - \frac{1}{14 x ^{7}}

Add a constant to the solution

= - \frac{1}{14 x ^{7}} + C

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