What is the integral from 0 to 33 of (x-1)^{-1/5} ?

The integral from 0 to 33 of (x-1)^{-1/5} is 75/4

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integral from 0 to 33 of (x-1)^{-1/5}

\int_{0}^{33} (x - 1)^{- \frac{1}{5}} d x

\frac{75}{4}

Decimal

18.75

Solution steps

\int_{0}^{33} (x - 1)^{- \frac{1}{5}} d x

Find undefined (singularity) points:

x = 1

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_{0}^{1} (x - 1)^{- \frac{1}{5}} d x + \int_{1}^{33} (x - 1)^{- \frac{1}{5}} d x

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

\int_{1}^{33} (x - 1)^{- \frac{1}{5}} d x = 20

= - \frac{5 ( - 1 ) ^{\frac{4}{5}}}{4} + 20

Simplify

- \frac{5 ( - 1 ) ^{\frac{4}{5}}}{4} + 20 : \frac{75}{4}

= \frac{75}{4}

What is the integral from 0 to 33 of (x-1)^{-1/5} ?
The integral from 0 to 33 of (x-1)^{-1/5} is 75/4