Integral of (x³+2x) dx

The solution

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  3              
  /              
 |               
 |  / 3      \   
 |  \x  + 2*x/ dx
 |               
/                
-1

$$\int\limits_{-1}^{3} \left(x^{3} + 2 x\right)\, dx$$

Integral(x^3 + 2*x, (x, -1, 3))

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:
  
  $\int 2 x\, dx = 2 \int x\, dx$
  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: $x^{2}$
The result is: $\frac{x^{4}}{4} + x^{2}$
Add the constant of integration:

$\frac{x^{4}}{4} + x^{2}+ \mathrm{constant}$

The answer is:

$\frac{x^{4}}{4} + x^{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

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Plot the graph f(x)

The answer [src]

$$28$$

Numerical answer [src]

28.0

28.0

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

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Integral of (x³+2x) dx

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The solution