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three x^3+3x
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Similar expressions
3x^3-3x

Solving integrals/ 3x^3+3x

Integral of 3x^3+3x dx

The solution

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

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

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

Detail solution

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

$\frac{3 x^{2} \left(x^{2} + 2\right)}{4}$
Add the constant of integration:

$\frac{3 x^{2} \left(x^{2} + 2\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{3 x^{2} \left(x^{2} + 2\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{3\,x^4}\over{4}}+{{3\,x^2}\over{2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

9/4

$${{9}\over{4}}$$

9/4

$$\frac{9}{4}$$

Упростить

Numerical answer [src]

2.25

2.25

The graph

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

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Integral of 3x^3+3x dx

Limits of integration:

The graph:

Piecewise:

The solution