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Identical expressions
x^ two + eleven
x squared plus 11
x to the power of two plus eleven
x2+11
x²+11
x to the power of 2+11
x^2+11dx
Similar expressions
x^2-11

Integral of x^2+11 dx

The solution

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  2             
  /             
 |              
 |  / 2     \   
 |  \x  + 11/ dx
 |              
/               
0

$$\int\limits_{0}^{2} \left(x^{2} + 11\right)\, dx$$

Integral(x^2 + 11, (x, 0, 2))

Detail solution

Integrate term-by-term:
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x^{2}\, dx = \frac{x^{3}}{3}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 11\, dx = 11 x$
The result is: $\frac{x^{3}}{3} + 11 x$
Now simplify:

$\frac{x \left(x^{2} + 33\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 33\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 33\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                            
 |                            3
 | / 2     \                 x 
 | \x  + 11/ dx = C + 11*x + --
 |                           3 
/

$$\int \left(x^{2} + 11\right)\, dx = C + \frac{x^{3}}{3} + 11 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

74/3

$$\frac{74}{3}$$

74/3

$$\frac{74}{3}$$

74/3

Numerical answer [src]

24.6666666666667

24.6666666666667

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

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Integral of x^2+11 dx

Limits of integration:

The graph:

Piecewise:

The solution