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Identical expressions
one / two x^2-2x+ five
1 divide by 2x squared minus 2x plus 5
one divide by two x squared minus 2x plus five
1/2x2-2x+5
1/2x²-2x+5
1/2x to the power of 2-2x+5
1 divide by 2x^2-2x+5
1/2x^2-2x+5dx
Similar expressions
1/2x^2+2x+5
1/2x^2-2x-5

Solving integrals/ 1/2x^2-2x+5

Integral of 1/2x^2-2x+5 dx

The solution

You have entered [src]

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

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

Simplify

Detail solution

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

$\frac{x \left(x^{2} - 6 x + 30\right)}{6}$
Add the constant of integration:

$\frac{x \left(x^{2} - 6 x + 30\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 6 x + 30\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{x^3}\over{6}}-x^2+5\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

25/6

$${{25}\over{6}}$$

25/6

$$\frac{25}{6}$$

Simplify

Numerical answer [src]

4.16666666666667

4.16666666666667

The graph

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

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Integral of 1/2x^2-2x+5 dx

Limits of integration:

The graph:

Piecewise:

The solution