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Identical expressions
three / two x^2-6x+ four
3 divide by 2x squared minus 6x plus 4
three divide by two x squared minus 6x plus four
3/2x2-6x+4
3/2x²-6x+4
3/2x to the power of 2-6x+4
3 divide by 2x^2-6x+4
3/2x^2-6x+4dx
Similar expressions
3/2x^2-6x-4
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Solving integrals/ 3/2x^2-6x+4

Integral of 3/2x^2-6x+4 dx

The solution

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

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

Integral(3*x^2/2 - 6*x + 4, (x, 0, 1))

Detail solution

Integrate term-by-term:
1. Integrate term-by-term:
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{3 x^{2}}{2}\, dx = \frac{3 \int x^{2}\, dx}{2}$
    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: $\frac{x^{3}}{2}$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \left(- 6 x\right)\, dx = - 6 \int x\, dx$
    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: $\frac{x^{3}}{2} - 3 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 4\, dx = 4 x$
The result is: $\frac{x^{3}}{2} - 3 x^{2} + 4 x$
Now simplify:

$\frac{x \left(x^{2} - 6 x + 8\right)}{2}$
Add the constant of integration:

$\frac{x \left(x^{2} - 6 x + 8\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 6 x + 8\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

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.

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Integral of 3/2x^2-6x+4 dx

Limits of integration:

The graph:

Piecewise:

The solution