Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of 7
Integral of sin^-1(x)
Integral of x*x
Integral of a
Identical expressions
(3x^ five -10x^ four +6x^ two -4x)dx
(3x to the power of 5 minus 10x to the power of 4 plus 6x squared minus 4x)dx
(3x to the power of five minus 10x to the power of four plus 6x to the power of two minus 4x)dx
(3x5-10x4+6x2-4x)dx
3x5-10x4+6x2-4xdx
(3x⁵-10x⁴+6x²-4x)dx
(3x to the power of 5-10x to the power of 4+6x to the power of 2-4x)dx
3x^5-10x^4+6x^2-4xdx
Similar expressions
(3x^5-10x^4+6x^2+4x)dx
(3x^5-10x^4-6x^2-4x)dx
(3x^5+10x^4+6x^2-4x)dx

Solving integrals/ (3x^5-10x^4+6x^2-4x)dx

Integral of (3x^5-10x^4+6x^2-4x)dx dx

The solution

You have entered [src]

  1                               
  /                               
 |                                
 |  /   5       4      2      \   
 |  \3*x  - 10*x  + 6*x  - 4*x/ dx
 |                                
/                                 
0

$$\int\limits_{0}^{1} \left(- 4 x + \left(6 x^{2} + \left(3 x^{5} - 10 x^{4}\right)\right)\right)\, dx$$

Integral(3*x^5 - 10*x^4 + 6*x^2 - 4*x, (x, 0, 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:
  
  $\int \left(- 4 x\right)\, dx = - 4 \int x\, dx$
  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: $- 2 x^{2}$
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int 6 x^{2}\, dx = 6 \int x^{2}\, dx$
    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: $2 x^{3}$
  1. Integrate term-by-term:
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int 3 x^{5}\, dx = 3 \int x^{5}\, dx$
      1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
        
        $\int x^{5}\, dx = \frac{x^{6}}{6}$
      So, the result is: $\frac{x^{6}}{2}$
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- 10 x^{4}\right)\, dx = - 10 \int x^{4}\, dx$
      1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
        
        $\int x^{4}\, dx = \frac{x^{5}}{5}$
      So, the result is: $- 2 x^{5}$
    The result is: $\frac{x^{6}}{2} - 2 x^{5}$
  The result is: $\frac{x^{6}}{2} - 2 x^{5} + 2 x^{3}$
The result is: $\frac{x^{6}}{2} - 2 x^{5} + 2 x^{3} - 2 x^{2}$
Now simplify:

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                                                            
 |                                       6                     
 | /   5       4      2      \          x       2      5      3
 | \3*x  - 10*x  + 6*x  - 4*x/ dx = C + -- - 2*x  - 2*x  + 2*x 
 |                                      2                      
/

$$\int \left(- 4 x + \left(6 x^{2} + \left(3 x^{5} - 10 x^{4}\right)\right)\right)\, dx = C + \frac{x^{6}}{2} - 2 x^{5} + 2 x^{3} - 2 x^{2}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-3/2

$$- \frac{3}{2}$$

-3/2

$$- \frac{3}{2}$$

-3/2

Numerical answer [src]

-1.5

-1.5

The graph

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

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of (3x^5-10x^4+6x^2-4x)dx dx

Limits of integration:

The graph:

Piecewise:

The solution