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Identical expressions
x- three / two x^2+5x- seven
x minus 3 divide by 2x squared plus 5x minus 7
x minus three divide by two x squared plus 5x minus seven
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x-3/2x²+5x-7
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x-3/2x^2+5x-7dx
Similar expressions
x-3/2x^2+5x+7
x+3/2x^2+5x-7
x-3/2x^2-5x-7

Integral of x-3/2x^2+5x-7 dx

The solution

You have entered [src]

  1                        
  /                        
 |                         
 |  /       2          \   
 |  |    3*x           |   
 |  |x - ---- + 5*x - 7| dx
 |  \     2            /   
 |                         
/                          
0

$$\int\limits_{0}^{1} \left(\left(5 x + \left(- \frac{3 x^{2}}{2} + x\right)\right) - 7\right)\, dx$$

Integral(x - 3*x^2/2 + 5*x - 7, (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:
    
    $\int 5 x\, dx = 5 \int x\, dx$
    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: $\frac{5 x^{2}}{2}$
  1. Integrate term-by-term:
    1. The integral of a constant times a function is the constant times the integral of the function:
      
      $\int \left(- \frac{3 x^{2}}{2}\right)\, dx = - \frac{3 \int x^{2}\, dx}{2}$
      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 $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x\, dx = \frac{x^{2}}{2}$
    The result is: $- \frac{x^{3}}{2} + \frac{x^{2}}{2}$
  The result is: $- \frac{x^{3}}{2} + 3 x^{2}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int \left(-7\right)\, dx = - 7 x$
The result is: $- \frac{x^{3}}{2} + 3 x^{2} - 7 x$
Now simplify:

$\frac{x \left(- x^{2} + 6 x - 14\right)}{2}$
Add the constant of integration:

$\frac{x \left(- x^{2} + 6 x - 14\right)}{2}+ \mathrm{constant}$

The answer is:

$\frac{x \left(- x^{2} + 6 x - 14\right)}{2}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                             
 |                                              
 | /       2          \                        3
 | |    3*x           |                   2   x 
 | |x - ---- + 5*x - 7| dx = C - 7*x + 3*x  - --
 | \     2            /                       2 
 |                                              
/

$$\int \left(\left(5 x + \left(- \frac{3 x^{2}}{2} + x\right)\right) - 7\right)\, dx = C - \frac{x^{3}}{2} + 3 x^{2} - 7 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-9/2

$$- \frac{9}{2}$$

-9/2

$$- \frac{9}{2}$$

-9/2

Numerical answer [src]

-4.5

-4.5

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

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Integral of x-3/2x^2+5x-7 dx

Limits of integration:

The graph:

Piecewise:

The solution