Integral of 1\(cbrt(x)) dx

The solution

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

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

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

Detail solution

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

Then let $du = \frac{dx}{3 x^{\frac{2}{3}}}$ and substitute $3 du$ :

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

$\frac{3 x^{\frac{2}{3}}}{2}$
Add the constant of integration:

$\frac{3 x^{\frac{2}{3}}}{2}+ \mathrm{constant}$

The answer is:

$\frac{3 x^{\frac{2}{3}}}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

3/2

$$\frac{3}{2}$$

3/2

$$\frac{3}{2}$$

3/2

Numerical answer [src]

1.49999999999969

1.49999999999969

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

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Integral of 1\(cbrt(x)) dx

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The solution