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Identical expressions
(x^ three +3x)
(x cubed plus 3x)
(x to the power of three plus 3x)
(x3+3x)
x3+3x
(x³+3x)
(x to the power of 3+3x)
x^3+3x
(x^3+3x)dx
Similar expressions
(x^3+3*x)/(x+3)
(x^3-3x)

Solving integrals/ (x^3+3x)

Integral of (x^3+3x) dx

The solution

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  2              
  /              
 |               
 |  / 3      \   
 |  \x  + 3*x/ dx
 |               
/                
0

$$\int\limits_{0}^{2} \left(x^{3} + 3 x\right)\, dx$$

Integral(x^3 + 3*x, (x, 0, 2))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{3}\, dx = \frac{x^{4}}{4}$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 3 x\, dx = 3 \int x\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x\, dx = \frac{x^{2}}{2}$
  So, the result is: $\frac{3 x^{2}}{2}$
The result is: $\frac{x^{4}}{4} + \frac{3 x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(x^{2} + 6\right)}{4}$
Add the constant of integration:

$\frac{x^{2} \left(x^{2} + 6\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(x^{2} + 6\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                      4      2
 | / 3      \          x    3*x 
 | \x  + 3*x/ dx = C + -- + ----
 |                     4     2  
/

$$\int \left(x^{3} + 3 x\right)\, dx = C + \frac{x^{4}}{4} + \frac{3 x^{2}}{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$10$$

Numerical answer [src]

10.0

10.0

The graph

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

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Integral of (x^3+3x) dx

Limits of integration:

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The solution