Mister Exam

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Integral of d{x}:
Integral of cosx
Integral of e^(x+1)
Integral of e^x²
Integral of -cos(2x)
Canonical form:
x^2+2*x+2
Factor squared:
x^2+2*x+2
Identical expressions
x^ two + two *x+ two
x squared plus 2 multiply by x plus 2
x to the power of two plus two multiply by x plus two
x2+2*x+2
x²+2*x+2
x to the power of 2+2*x+2
x^2+2x+2
x2+2x+2
x^2+2*x+2dx
Similar expressions
(2*x+3)/(x^2+2*x+2)
x^2-2*x+2
x^2+2*x-2

Solving integrals/ x^2+2*x+2

Integral of x^2+2*x+2 dx

The solution

You have entered [src]

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

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

Integral(x^2 + 2*x + 2, (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:
  
  $\int 2\, dx = 2 x$
The result is: $\frac{x^{3}}{3} + x^{2} + 2 x$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

10/3

$$\frac{10}{3}$$

10/3

$$\frac{10}{3}$$

10/3

Numerical answer [src]

3.33333333333333

3.33333333333333

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+2*x+2 dx

Limits of integration:

The graph:

Piecewise:

The solution