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

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

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

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

3 + 3 \cdot 2^{\frac{1}{3}}

Decimal Notation

6.77976 \dots

Solution steps

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

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

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

= - 3 (- 1)^{\frac{1}{3}} + 3 \cdot 2^{\frac{1}{3}}

Simplify

- 3 (- 1)^{\frac{1}{3}} + 3 \cdot 2^{\frac{1}{3}} : 3 + 3 \cdot 2^{\frac{1}{3}}

= 3 + 3 \cdot 2^{\frac{1}{3}}

y^{^{'}} = \frac{t ^{3} + 19 t ^{3} y}{t}

\frac{\partial}{\partial y} (- yz)

x \to - 7 lim (\frac{1}{x})

x \to 9 lim (cos (\frac{π x}{3}))

y = x^{2} - 2 x

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