What is the integral from 3 to 5 of 8x^{-3} ?

The integral from 3 to 5 of 8x^{-3} is 64/225

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integral from 3 to 5 of 8x^{-3}

\int_{3}^{5} 8 x^{- 3} d x

\frac{64}{225}

Decimal Notation

0.28444 \dots

Solution steps

\int_{3}^{5} 8 x^{- 3} d x

Take the constant out:

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

= 8 \cdot \int_{3}^{5} x^{- 3} d x

Apply the Power Rule

: [- \frac{1}{2 x ^{2}}]_{3}^{5}

= 8 [- \frac{1}{2 x ^{2}}]_{3}^{5}

Compute the boundaries:

\frac{8}{225}

= 8 \cdot \frac{8}{225}

Simplify

= \frac{64}{225}

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What is the integral from 3 to 5 of 8x^{-3} ?
The integral from 3 to 5 of 8x^{-3} is 64/225