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Graphing y =:
x^3+x^(1/3)
Identical expressions
x^ three +x^(one / three)
x cubed plus x to the power of (1 divide by 3)
x to the power of three plus x to the power of (one divide by three)
x3+x(1/3)
x3+x1/3
x³+x^(1/3)
x to the power of 3+x to the power of (1/3)
x^3+x^1/3
x^3+x^(1 divide by 3)
x^3+x^(1/3)dx
Similar expressions
x^3-x^(1/3)

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

Integral of x^3+x^(1/3) dx

The solution

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

$$\int\limits_{0}^{1} \left(\sqrt[3]{x} + x^{3}\right)\, dx$$

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

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \sqrt[3]{x}\, dx = \frac{3 x^{\frac{4}{3}}}{4}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
The result is: $\frac{3 x^{\frac{4}{3}}}{4} + \frac{x^{4}}{4}$
Add the constant of integration:

$\frac{3 x^{\frac{4}{3}}}{4} + \frac{x^{4}}{4}+ \mathrm{constant}$

The answer is:

$\frac{3 x^{\frac{4}{3}}}{4} + \frac{x^{4}}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                 
 |                        4      4/3
 | / 3   3 ___\          x    3*x   
 | \x  + \/ x / dx = C + -- + ------
 |                       4      4   
/

$$\int \left(\sqrt[3]{x} + x^{3}\right)\, dx = C + \frac{3 x^{\frac{4}{3}}}{4} + \frac{x^{4}}{4}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1$$

Numerical answer [src]

1.0

1.0

The graph

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

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Identical expressions

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Integral of x^3+x^(1/3) dx

Limits of integration:

The graph:

Piecewise:

The solution