What is the integral from 0 to 33 of 3(x-1)^{-1/5} ?

The integral from 0 to 33 of 3(x-1)^{-1/5} is 225/4

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integral from 0 to 33 of 3(x-1)^{-1/5}

\int_{0}^{33} 3 (x - 1)^{- \frac{1}{5}} d x

\frac{225}{4}

Decimal Notation

56.25

Solution steps

\int_{0}^{33} 3 (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} 3 (x - 1)^{- \frac{1}{5}} d x + \int_{1}^{33} 3 (x - 1)^{- \frac{1}{5}} d x

\int_{0}^{1} 3 (x - 1)^{- \frac{1}{5}} d x = - \frac{15 ( - 1 ) ^{\frac{4}{5}}}{4}

\int_{1}^{33} 3 (x - 1)^{- \frac{1}{5}} d x = 60

= - \frac{15 ( - 1 ) ^{\frac{4}{5}}}{4} + 60

Simplify

- \frac{15 ( - 1 ) ^{\frac{4}{5}}}{4} + 60 : \frac{225}{4}

= \frac{225}{4}

x y \frac{d y}{d x} = 2 y^{2} - x^{2}

\int 5 x^{\frac{1}{2}} d x

\frac{\partial}{\partial y} (\frac{x ^{2} - y ^{2}}{x y})

\int \frac{2 x}{x ^{2} + 5} d x

f (x) = x - x^{3}

What is the integral from 0 to 33 of 3(x-1)^{-1/5} ?
The integral from 0 to 33 of 3(x-1)^{-1/5} is 225/4