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Derivative of:
2*x^2+x
Graphing y =:
2*x^2+x
Factor polynomial:
2*x^2+x
Identical expressions
two *x^ two +x
2 multiply by x squared plus x
two multiply by x to the power of two plus x
2*x2+x
2*x²+x
2*x to the power of 2+x
2x^2+x
2x2+x
2*x^2+xdx
Similar expressions
(x^3-2x^2+x+3)
2*x^2-x

Integral of 2*x^2+x dx

The solution

You have entered [src]

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

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

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

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 $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int x\, dx = \frac{x^{2}}{2}$
The result is: $\frac{2 x^{3}}{3} + \frac{x^{2}}{2}$
Now simplify:

$\frac{x^{2} \left(4 x + 3\right)}{6}$
Add the constant of integration:

$\frac{x^{2} \left(4 x + 3\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(4 x + 3\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

4/3

$$\frac{4}{3}$$

4/3

$$\frac{4}{3}$$

4/3

Numerical answer [src]

1.33333333333333

1.33333333333333

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

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Integral of 2*x^2+x dx

Limits of integration:

The graph:

Piecewise:

The solution