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Similar expressions
1/((2+x)^(2/3))

Integral of 1/((2-x)^(2/3)) dx

The solution

You have entered [src]

  6              
  /              
 |               
 |      1        
 |  ---------- dx
 |         2/3   
 |  (2 - x)      
 |               
/                
2

$$\int\limits_{2}^{6} \frac{1}{\left(2 - x\right)^{\frac{2}{3}}}\, dx$$

Integral(1/((2 - x)^(2/3)), (x, 2, 6))

Detail solution

Let $u = \left(2 - x\right)^{\frac{2}{3}}$ .

Then let $du = - \frac{2 dx}{3 \sqrt[3]{2 - x}}$ and substitute $- \frac{3 du}{2}$ :

$\int \left(- \frac{3}{2 \sqrt{u}}\right)\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{\sqrt{u}}\, du = - \frac{3 \int \frac{1}{\sqrt{u}}\, du}{2}$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{\sqrt{u}}\, du = 2 \sqrt{u}$
  So, the result is: $- 3 \sqrt{u}$
Now substitute $u$ back in:

$- 3 \sqrt[3]{2 - x}$
Add the constant of integration:

$- 3 \sqrt[3]{2 - x}+ \mathrm{constant}$

The answer is:

$- 3 \sqrt[3]{2 - x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                               
 |                                
 |     1                 3 _______
 | ---------- dx = C - 3*\/ 2 - x 
 |        2/3                     
 | (2 - x)                        
 |                                
/

$$\int \frac{1}{\left(2 - x\right)^{\frac{2}{3}}}\, dx = C - 3 \sqrt[3]{2 - x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

   3 ____  2/3
-3*\/ -1 *2

$$- 3 \sqrt[3]{-1} \cdot 2^{\frac{2}{3}}$$

   3 ____  2/3
-3*\/ -1 *2

$$- 3 \sqrt[3]{-1} \cdot 2^{\frac{2}{3}}$$

-3*(-1)^(1/3)*2^(2/3)

Numerical answer [src]

(-2.38110059391664 - 4.12418720659605j)

(-2.38110059391664 - 4.12418720659605j)

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

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Identical expressions

Similar expressions

Integral of 1/((2-x)^(2/3)) dx

Limits of integration:

The graph:

Piecewise:

The solution