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Similar expressions
2/(x^(2/3))

Integral of 2/(x^(-2/3)) dx

The solution

You have entered [src]

  1          
  /          
 |           
 |    2      
 |  ------ dx
 |  / 1  \   
 |  |----|   
 |  | 2/3|   
 |  \x   /   
 |           
/            
0

$$\int\limits_{0}^{1} \frac{2}{\frac{1}{x^{\frac{2}{3}}}}\, dx$$

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

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{2}{\frac{1}{x^{\frac{2}{3}}}}\, dx = 2 \int \frac{1}{\frac{1}{x^{\frac{2}{3}}}}\, dx$
1. Let $u = \frac{1}{x^{\frac{2}{3}}}$ .
  
  Then let $du = - \frac{2 dx}{3 x^{\frac{5}{3}}}$ and substitute $- \frac{3 du}{2}$ :
  
  $\int \left(- \frac{3}{2 u^{\frac{7}{2}}}\right)\, du$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{1}{u^{\frac{7}{2}}}\, du = - \frac{3 \int \frac{1}{u^{\frac{7}{2}}}\, du}{2}$
    1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int \frac{1}{u^{\frac{7}{2}}}\, du = - \frac{2}{5 u^{\frac{5}{2}}}$
    So, the result is: $\frac{3}{5 u^{\frac{5}{2}}}$
  Now substitute $u$ back in:
  
  $\frac{3 x^{\frac{5}{3}}}{5}$
So, the result is: $\frac{6 x^{\frac{5}{3}}}{5}$
Add the constant of integration:

$\frac{6 x^{\frac{5}{3}}}{5}+ \mathrm{constant}$

The answer is:

$\frac{6 x^{\frac{5}{3}}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                      
 |                    5/3
 |   2             6*x   
 | ------ dx = C + ------
 | / 1  \            5   
 | |----|                
 | | 2/3|                
 | \x   /                
 |                       
/

$$\int \frac{2}{\frac{1}{x^{\frac{2}{3}}}}\, dx = C + \frac{6 x^{\frac{5}{3}}}{5}$$

Simplify

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Plot the graph f(x)

The answer [src]

6/5

$$\frac{6}{5}$$

6/5

$$\frac{6}{5}$$

6/5

Numerical answer [src]

1.2

1.2

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

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Identical expressions

Similar expressions

Integral of 2/(x^(-2/3)) dx

Limits of integration:

The graph:

Piecewise:

The solution