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Integral of x/(2*x+1)
Graphing y =:
x^2+4x+6
Canonical form:
x^2+4x+6
Identical expressions
x^ two +4x+ six
x squared plus 4x plus 6
x to the power of two plus 4x plus six
x2+4x+6
x²+4x+6
x to the power of 2+4x+6
x^2+4x+6dx
Similar expressions
x^2-4x+6
x^2+4x-6

Integral of x^2+4x+6 dx

The solution

You have entered [src]

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 |  \x  + 4*x + 6/ dx
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0

$$\int\limits_{0}^{1} \left(\left(x^{2} + 4 x\right) + 6\right)\, dx$$

Integral(x^2 + 4*x + 6, (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:
    
    $\int 4 x\, dx = 4 \int x\, dx$
    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: $2 x^{2}$
  The result is: $\frac{x^{3}}{3} + 2 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 6\, dx = 6 x$
The result is: $\frac{x^{3}}{3} + 2 x^{2} + 6 x$
Now simplify:

$\frac{x \left(x^{2} + 6 x + 18\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} + 6 x + 18\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} + 6 x + 18\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                       
 |                                       3
 | / 2          \             2         x 
 | \x  + 4*x + 6/ dx = C + 2*x  + 6*x + --
 |                                      3 
/

$$\int \left(\left(x^{2} + 4 x\right) + 6\right)\, dx = C + \frac{x^{3}}{3} + 2 x^{2} + 6 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

25/3

$$\frac{25}{3}$$

25/3

$$\frac{25}{3}$$

25/3

Numerical answer [src]

8.33333333333333

8.33333333333333

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

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Integral of x^2+4x+6 dx

Limits of integration:

The graph:

Piecewise:

The solution