What is the integral from 0 to 2 of 1/((x-2)^{3/5)} ?

The integral from 0 to 2 of 1/((x-2)^{3/5)} is -(5(-1)^{2/5})/(2^{3/5)}

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integral from 0 to 2 of 1/((x-2)^{3/5)}

\int_{0}^{2} \frac{1}{( x - 2 ) ^{\frac{3}{5}}} d x

- \frac{5 ( - 1 ) ^{\frac{2}{5}}}{2 ^{\frac{3}{5}}}

Solution steps

\int_{0}^{2} \frac{1}{( x - 2 ) ^{\frac{3}{5}}} d x

Apply u-substitution

: \int_{- 2}^{0} \frac{1}{u ^{\frac{3}{5}}} d u

= \int_{- 2}^{0} \frac{1}{u ^{\frac{3}{5}}} d u

Apply the Power Rule

: [\frac{5}{2} u^{\frac{2}{5}}]_{- 2}^{0}

= [\frac{5}{2} u^{\frac{2}{5}}]_{- 2}^{0}

Compute the boundaries:

- \frac{5 ( - 1 ) ^{\frac{2}{5}}}{2 ^{\frac{3}{5}}}

= - \frac{5 ( - 1 ) ^{\frac{2}{5}}}{2 ^{\frac{3}{5}}}

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What is the integral from 0 to 2 of 1/((x-2)^{3/5)} ?
The integral from 0 to 2 of 1/((x-2)^{3/5)} is -(5(-1)^{2/5})/(2^{3/5)}