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Identical expressions
(five -18x^ two)/ three
(5 minus 18x squared ) divide by 3
(five minus 18x to the power of two) divide by three
(5-18x2)/3
5-18x2/3
(5-18x²)/3
(5-18x to the power of 2)/3
5-18x^2/3
(5-18x^2) divide by 3
(5-18x^2)/3dx
Similar expressions
(5+18x^2)/3

Solving integrals/ (5-18x^2)/3

Integral of (5-18x^2)/3 dx

The solution

You have entered [src]

  1             
  /             
 |              
 |          2   
 |  5 - 18*x    
 |  --------- dx
 |      3       
 |              
/               
0

$$\int\limits_{0}^{1} \frac{- 18 x^{2} + 5}{3}\, dx$$

Integral(5 - 18*x^2/3, (x, 0, 1))

Detail solution

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

$\int \frac{5 - 18 x^{2}}{3}\, dx = \frac{\int \left(5 - 18 x^{2}\right)\, dx}{3}$
1. Integrate term-by-term:
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int 5\, dx = 5 x$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 18 x^{2}\right)\, dx = - \int 18 x^{2}\, dx$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int 18 x^{2}\, dx = 18 \int x^{2}\, dx$
      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: $6 x^{3}$
    So, the result is: $- 6 x^{3}$
  The result is: $- 6 x^{3} + 5 x$
So, the result is: $- 2 x^{3} + \frac{5 x}{3}$
Now simplify:

$\frac{x \left(5 - 6 x^{2}\right)}{3}$
Add the constant of integration:

$\frac{x \left(5 - 6 x^{2}\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(5 - 6 x^{2}\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                             
 |                              
 |         2                    
 | 5 - 18*x              3   5*x
 | --------- dx = C - 2*x  + ---
 |     3                      3 
 |                              
/

$$5\,x-2\,x^3$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-1/3

$$3$$

-1/3

$$- \frac{1}{3}$$

Упростить

Numerical answer [src]

-0.333333333333333

-0.333333333333333

The graph

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

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Integral of (5-18x^2)/3 dx

Limits of integration:

The graph:

Piecewise:

The solution