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

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

Popular >

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

\int_{0}^{2} \frac{5}{( x - 1 ) ^{\frac{1}{3}}} d x

0

Solution steps

\int_{0}^{2} \frac{5}{( x - 1 ) ^{\frac{1}{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{5}{( x - 1 ) ^{\frac{1}{3}}} d x + \int_{1}^{2} \frac{5}{( x - 1 ) ^{\frac{1}{3}}} d x

\int_{0}^{1} \frac{5}{( x - 1 ) ^{\frac{1}{3}}} d x = - \frac{15 ( - 1 ) ^{\frac{2}{3}}}{2}

\int_{1}^{2} \frac{5}{( x - 1 ) ^{\frac{1}{3}}} d x = \frac{15}{2}

= - \frac{15 ( - 1 ) ^{\frac{2}{3}}}{2} + \frac{15}{2}

Simplify

- \frac{15 ( - 1 ) ^{\frac{2}{3}}}{2} + \frac{15}{2} : 0

= 0

x \to 2 lim (\frac{x ^{2} + 5}{x - 2})

\frac{\partial}{\partial y} (8 x y + 8 y^{2} - 2 x + 2 y - 1)

\frac{d}{d x} ((1 + \frac{5}{x})^{x})

\frac{\partial}{\partial z} (x e^{2 y + 3 z})

\frac{\partial}{\partial x} (ln (\frac{x}{2 y}))

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