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Similar expressions
1/18(2x^2-x)

Solving integrals/ 1/18(2x^2+x)

Integral of 1/18(2x^2+x) dx

The solution

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  4            
  /            
 |             
 |     2       
 |  2*x  + x   
 |  -------- dx
 |     18      
 |             
/              
1

$$\int\limits_{1}^{4} \frac{2 x^{2} + x}{18}\, dx$$

Integral((2*x^2 + x)/18, (x, 1, 4))

Detail solution

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{2 x^{2} + x}{18}\, dx = \frac{\int \left(2 x^{2} + x\right)\, dx}{18}$
1. 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: $\frac{2 x^{3}}{3} + \frac{x^{2}}{2}$
So, the result is: $\frac{x^{3}}{27} + \frac{x^{2}}{36}$
Now simplify:

$\frac{x^{2} \left(4 x + 3\right)}{108}$
Add the constant of integration:

$\frac{x^{2} \left(4 x + 3\right)}{108}+ \mathrm{constant}$

The answer is:

$\frac{x^{2} \left(4 x + 3\right)}{108}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                         
 |                          
 |    2               3    2
 | 2*x  + x          x    x 
 | -------- dx = C + -- + --
 |    18             27   36
 |                          
/

$$\int \frac{2 x^{2} + x}{18}\, dx = C + \frac{x^{3}}{27} + \frac{x^{2}}{36}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

11/4

$$\frac{11}{4}$$

11/4

$$\frac{11}{4}$$

11/4

Numerical answer [src]

2.75

2.75

The graph

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

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Integral of 1/18(2x^2+x) dx

Limits of integration:

The graph:

Piecewise:

The solution