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Integral of d{x}:
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Integral of x*dx/(x^2+1)
Integral of z
Graphing y =:
x^2+6*x+10
Factor polynomial:
x^2+6*x+10
Identical expressions
x^ two + six *x+ ten
x squared plus 6 multiply by x plus 10
x to the power of two plus six multiply by x plus ten
x2+6*x+10
x²+6*x+10
x to the power of 2+6*x+10
x^2+6x+10
x2+6x+10
x^2+6*x+10dx
Similar expressions
x^2-6*x+10
x^2+6*x-10

Integral of x^2+6*x+10 dx

The solution

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  2                   
  /                   
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 |  / 2           \   
 |  \x  + 6*x + 10/ dx
 |                    
/                     
-1

$$\int\limits_{-1}^{2} \left(\left(x^{2} + 6 x\right) + 10\right)\, dx$$

Integral(x^2 + 6*x + 10, (x, -1, 2))

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:
    
    $\int 6 x\, dx = 6 \int x\, dx$
    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: $3 x^{2}$
  The result is: $\frac{x^{3}}{3} + 3 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 10\, dx = 10 x$
The result is: $\frac{x^{3}}{3} + 3 x^{2} + 10 x$
Now simplify:

$\frac{x \left(x^{2} + 9 x + 30\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 9 x + 30\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 9 x + 30\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                         
 |                                         3
 | / 2           \             2          x 
 | \x  + 6*x + 10/ dx = C + 3*x  + 10*x + --
 |                                        3 
/

$$\int \left(\left(x^{2} + 6 x\right) + 10\right)\, dx = C + \frac{x^{3}}{3} + 3 x^{2} + 10 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$42$$

Numerical answer [src]

42.0

42.0

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

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Integral of x^2+6*x+10 dx

Limits of integration:

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Piecewise:

The solution