What is the integral from 9 to 15 of (x-8)^{-2/3} ?

The integral from 9 to 15 of (x-8)^{-2/3} is 3*7^{1/3}-3

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integral from 9 to 15 of (x-8)^{-2/3}

\int_{9}^{15} (x - 8)^{- \frac{2}{3}} d x

3 \cdot 7^{\frac{1}{3}} - 3

Decimal

2.73879 \dots

Solution steps

\int_{9}^{15} (x - 8)^{- \frac{2}{3}} d x

Apply u-substitution

: \int_{1}^{7} \frac{1}{u ^{\frac{2}{3}}} d u

= \int_{1}^{7} \frac{1}{u ^{\frac{2}{3}}} d u

Apply the Power Rule

: [3 u^{\frac{1}{3}}]_{1}^{7}

= [3 u^{\frac{1}{3}}]_{1}^{7}

Compute the boundaries:

3 \cdot 7^{\frac{1}{3}} - 3

= 3 \cdot 7^{\frac{1}{3}} - 3

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What is the integral from 9 to 15 of (x-8)^{-2/3} ?
The integral from 9 to 15 of (x-8)^{-2/3} is 3*7^{1/3}-3