What is the integral from 2 to x of 384x^{-7} ?

The integral from 2 to x of 384x^{-7} is -(64)/(x^6)+1

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integral from 2 to x of 384x^{-7}

\int_{2}^{x} 384 x^{- 7} d x

- \frac{64}{x ^{6}} + 1

Solution steps

\int_{2}^{x} 384 x^{- 7} d x

Take the constant out:

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

= 384 \cdot \int_{2}^{x} x^{- 7} d x

Apply the Power Rule

: [- \frac{1}{6 x ^{6}}]_{2}^{x}

= 384 [- \frac{1}{6 x ^{6}}]_{2}^{x}

Compute the boundaries:

- \frac{1}{6 x ^{6}} + \frac{1}{384}

= 384 (- \frac{1}{6 x ^{6}} + \frac{1}{384})

Simplify

= - \frac{64}{x ^{6}} + 1

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What is the integral from 2 to x of 384x^{-7} ?
The integral from 2 to x of 384x^{-7} is -(64)/(x^6)+1