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Integral of d{x}:
Integral of 1/(2+cos(x))
Integral of √((1-x)/(1+x))
Integral of dz
Integral of cos(x)*exp(x)
Factor squared:
x^2+x+3
Graphing y =:
x^2+x+3
Canonical form:
x^2+x+3
Identical expressions
x^ two +x+ three
x squared plus x plus 3
x to the power of two plus x plus three
x2+x+3
x²+x+3
x to the power of 2+x+3
x^2+x+3dx
Similar expressions
x^2+x-3
x^2-x+3

Solving integrals/ x^2+x+3

Integral of x^2+x+3 dx

The solution

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

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

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

Detail solution

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

$\frac{x \left(2 x^{2} + 3 x + 18\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} + 3 x + 18\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} + 3 x + 18\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

76/3

$$\frac{76}{3}$$

76/3

$$\frac{76}{3}$$

76/3

Numerical answer [src]

25.3333333333333

25.3333333333333

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^2+x+3 dx

Limits of integration:

The graph:

Piecewise:

The solution