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

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

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

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

3

Solution steps

\int_{0}^{1} \frac{1}{( 1 - x ) ^{\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

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Simplify

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

Compute the boundaries:

3

= 3

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