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

Solving integrals/ x^3+x+3

Integral of x^3+x+3 dx

The solution

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

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

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

Detail solution

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

$\frac{x \left(x^{3} + 2 x + 12\right)}{4}$
Add the constant of integration:

$\frac{x \left(x^{3} + 2 x + 12\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} + 2 x + 12\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

-36

$$-36$$

-36

$$-36$$

Упростить

Numerical answer [src]

-36.0

-36.0

The graph

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

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Integral of x^3+x+3 dx

Limits of integration:

The graph:

Piecewise:

The solution