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Graphing y =:
2x^2+6x
Derivative of:
2x^2+6x
Identical expressions
two x^2+6x
2x squared plus 6x
two x squared plus 6x
2x2+6x
2x²+6x
2x to the power of 2+6x
2x^2+6xdx
Similar expressions
2x^2-6x

Integral of 2x^2+6x dx

The solution

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  6                
  /                
 |                 
 |  /   2      \   
 |  \2*x  + 6*x/ dx
 |                 
/                  
0

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

Integral(2*x^2 + 6*x, (x, 0, 6))

Detail solution

Integrate term-by-term:
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int 2 x^{2}\, dx = 2 \int x^{2}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int x^{2}\, dx = \frac{x^{3}}{3}$
  So, the result is: $\frac{2 x^{3}}{3}$
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: $\frac{2 x^{3}}{3} + 3 x^{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$252$$

Numerical answer [src]

252.0

252.0

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

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Integral of 2x^2+6x dx

Limits of integration:

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Piecewise:

The solution