What is the integral from 1 to 2 of 1/((x-2)^{2/3)} ?

The integral from 1 to 2 of 1/((x-2)^{2/3)} is -3(-1)^{1/3}

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integral from 1 to 2 of 1/((x-2)^{2/3)}

\int_{1}^{2} \frac{1}{( x - 2 ) ^{\frac{2}{3}}} d x

- 3 (- 1)^{\frac{1}{3}}

Solution steps

\int_{1}^{2} \frac{1}{( x - 2 ) ^{\frac{2}{3}}} d x

Apply u-substitution

: \int_{- 1}^{0} \frac{1}{u ^{\frac{2}{3}}} d u

= \int_{- 1}^{0} \frac{1}{u ^{\frac{2}{3}}} d u

Apply the Power Rule

: [3 u^{\frac{1}{3}}]_{- 1}^{0}

= [3 u^{\frac{1}{3}}]_{- 1}^{0}

Compute the boundaries:

- 3 (- 1)^{\frac{1}{3}}

= - 3 (- 1)^{\frac{1}{3}}

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