What is the integral from 0 to 4 of 1/((4-x)^{2/5)} ?

The integral from 0 to 4 of 1/((4-x)^{2/5)} is (5*4^{3/5})/3

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integral from 0 to 4 of 1/((4-x)^{2/5)}

\int_{0}^{4} \frac{1}{( 4 - x ) ^{\frac{2}{5}}} d x

\frac{5 \cdot 4 ^{\frac{3}{5}}}{3}

Decimal Notation

3.82899 \dots

Solution steps

\int_{0}^{4} \frac{1}{( 4 - x ) ^{\frac{2}{5}}} d x

Apply u-substitution

: \int_{4}^{0} - \frac{1}{u ^{\frac{2}{5}}} d u

= \int_{4}^{0} - \frac{1}{u ^{\frac{2}{5}}} d u

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

= - \int_{0}^{4} - \frac{1}{u ^{\frac{2}{5}}} d u

Take the constant out:

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

= - (- \int_{0}^{4} \frac{1}{u ^{\frac{2}{5}}} d u)

Apply the Power Rule

: [\frac{5}{3} u^{\frac{3}{5}}]_{0}^{4}

= - (- [\frac{5}{3} u^{\frac{3}{5}}]_{0}^{4})

Simplify

= [\frac{5}{3} u^{\frac{3}{5}}]_{0}^{4}

Compute the boundaries:

4^{\frac{3}{5}} \cdot \frac{5}{3}

= 4^{\frac{3}{5}} \cdot \frac{5}{3}

Simplify

= \frac{5 \cdot 4 ^{\frac{3}{5}}}{3}

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What is the integral from 0 to 4 of 1/((4-x)^{2/5)} ?
The integral from 0 to 4 of 1/((4-x)^{2/5)} is (5*4^{3/5})/3