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Integral of d{x}:
Integral of x^(-1/2)
Integral of sin²xcos²x
Integral of x*2^(-x)
Integral of y^(-2/3)
Identical expressions
y^(- two / three)
y to the power of ( minus 2 divide by 3)
y to the power of ( minus two divide by three)
y(-2/3)
y-2/3
y^-2/3
y^(-2 divide by 3)
Similar expressions
y^(2/3)

Solving integrals/ y^(-2/3)

Integral of y^(-2/3) dy

The solution

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$$\int\limits_{0}^{1} \frac{1}{y^{\frac{2}{3}}}\, dy$$

Integral(y^(-2/3), (y, 0, 1))

Detail solution

The integral of $y^{n}$ is $\frac{y^{n + 1}}{n + 1}$ when $n \neq -1$ :

$\int \frac{1}{y^{\frac{2}{3}}}\, dy = 3 \sqrt[3]{y}$
Add the constant of integration:

$3 \sqrt[3]{y}+ \mathrm{constant}$

The answer is:

$3 \sqrt[3]{y}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                     
 |                      
 |  1              3 ___
 | ---- dy = C + 3*\/ y 
 |  2/3                 
 | y                    
 |                      
/

$$\int \frac{1}{y^{\frac{2}{3}}}\, dy = C + 3 \sqrt[3]{y}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$3$$

Numerical answer [src]

2.9999987600149

2.9999987600149

The graph

Use the examples entering the upper and lower limits of integration.

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Identical expressions

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Integral of y^(-2/3) dy

Limits of integration:

The graph:

Piecewise:

The solution