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

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

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

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

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

Decimal Notation

1.76028 \dots

Solution steps

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

Find undefined (singularity) points:

x = 2

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{1}^{2} \frac{1}{( x - 2 ) ^{\frac{1}{5}}} d x + \int_{2}^{5} \frac{1}{( x - 2 ) ^{\frac{1}{5}}} d x

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

\int_{2}^{5} \frac{1}{( x - 2 ) ^{\frac{1}{5}}} d x = \frac{5 \cdot 3 ^{\frac{4}{5}}}{4}

= - \frac{5 ( - 1 ) ^{\frac{4}{5}}}{4} + \frac{5 \cdot 3 ^{\frac{4}{5}}}{4}

5 (- 1)^{\frac{4}{5}} = 5

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

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