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

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

The solution

You have entered [src]

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

$$\int\limits_{0}^{1} \frac{1}{\sqrt[3]{3 x - 2}}\, dx$$

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

Detail solution

Let $u = \sqrt[3]{3 x - 2}$ .

Then let $du = \frac{dx}{\left(3 x - 2\right)^{\frac{2}{3}}}$ and substitute $du$ :

$\int u\, du$
1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int u\, du = \frac{u^{2}}{2}$
Now substitute $u$ back in:

$\frac{\left(3 x - 2\right)^{\frac{2}{3}}}{2}$
Now simplify:

$\frac{\left(3 x - 2\right)^{\frac{2}{3}}}{2}$
Add the constant of integration:

$\frac{\left(3 x - 2\right)^{\frac{2}{3}}}{2}+ \mathrm{constant}$

The answer is:

$\frac{\left(3 x - 2\right)^{\frac{2}{3}}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

        2/3
1   (-2)   
- - -------
2      2

$$\frac{1}{2} - \frac{\left(-2\right)^{\frac{2}{3}}}{2}$$

        2/3
1   (-2)   
- - -------
2      2

$$\frac{1}{2} - \frac{\left(-2\right)^{\frac{2}{3}}}{2}$$

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

Numerical answer [src]

(0.931192485524267 - 0.804542879268542j)

(0.931192485524267 - 0.804542879268542j)

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

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

Limits of integration:

The graph:

Piecewise:

The solution