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Identical expressions
x^ two +2x+ ten
x squared plus 2x plus 10
x to the power of two plus 2x plus ten
x2+2x+10
x²+2x+10
x to the power of 2+2x+10
x^2+2x+10dx
Similar expressions
x^2+2x-10
x^2-2x+10

Solving integrals/ x^2+2x+10

Integral of x^2+2x+10 dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  / 2           \   
 |  \x  + 2*x + 10/ dx
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(\left(x^{2} + 2 x\right) + 10\right)\, dx$$

Integral(x^2 + 2*x + 10, (x, 0, 1))

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 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: $\frac{x^{3}}{3} + x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 10\, dx = 10 x$
The result is: $\frac{x^{3}}{3} + x^{2} + 10 x$
Now simplify:

$\frac{x \left(x^{2} + 3 x + 30\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 3 x + 30\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 3 x + 30\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                       3
 | / 2           \           2          x 
 | \x  + 2*x + 10/ dx = C + x  + 10*x + --
 |                                      3 
/

$$\int \left(\left(x^{2} + 2 x\right) + 10\right)\, dx = C + \frac{x^{3}}{3} + x^{2} + 10 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

34/3

$$\frac{34}{3}$$

34/3

$$\frac{34}{3}$$

34/3

Numerical answer [src]

11.3333333333333

11.3333333333333

The graph

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

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Integral of x^2+2x+10 dx

Limits of integration:

The graph:

Piecewise:

The solution