Mister Exam

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

Solving integrals/ x^2+x+2

Integral of x^2+x+2 dx

The solution

You have entered [src]

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

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

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

$\frac{x \left(2 x^{2} + 3 x + 12\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} + 3 x + 12\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} + 3 x + 12\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

17/6

$$\frac{17}{6}$$

17/6

$$\frac{17}{6}$$

17/6

Numerical answer [src]

2.83333333333333

2.83333333333333

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+2 dx

Limits of integration:

The graph:

Piecewise:

The solution