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x^(-1/3)
Solving integrals/ x^(-1/3)

Integral of x^(-1/3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1         
  /         
 |          
 |    1     
 |  ----- dx
 |  3 ___   
 |  \/ x    
 |          
/           
0
∫011x3 dx\int\limits_{0}^{1} \frac{1}{\sqrt[3]{x}}\, dx 
Integral(x^(-1/3), (x, 0, 1))
Detail solution

  1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

    ∫1x3 dx=3x232\int \frac{1}{\sqrt[3]{x}}\, dx = \frac{3 x^{\frac{2}{3}}}{2}

  2. Add the constant of integration:

    3x232+constant\frac{3 x^{\frac{2}{3}}}{2}+ \mathrm{constant}

The answer is:

3x232+constant\frac{3 x^{\frac{2}{3}}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                     
 |                   2/3
 |   1            3*x   
 | ----- dx = C + ------
 | 3 ___            2   
 | \/ x                 
 |                      
/
∫1x3 dx=C+3x232\int \frac{1}{\sqrt[3]{x}}\, dx = C + \frac{3 x^{\frac{2}{3}}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90020
Plot the graph f(x)
The answer [src] 
3/2
32\frac{3}{2} 
=
= 
3/2
32\frac{3}{2} 
3/2
Numerical answer [src] 
1.49999999999969
1.49999999999969
The graph
Integral of x^(-1/3) dx

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

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