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Integral of d{x}:
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Integral of 1/(x^2+2*x+5)
Graphing y =:
x^2-5x+4
Derivative of:
x^2-5x+4
Identical expressions
x^ two -5x+ four
x squared minus 5x plus 4
x to the power of two minus 5x plus four
x2-5x+4
x²-5x+4
x to the power of 2-5x+4
x^2-5x+4dx
Similar expressions
x^2+5x+4
x^2-5x-4

Solving integrals/ x^2-5x+4

Integral of x^2-5x+4 dx

The solution

You have entered [src]

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

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

Integral(x^2 - 5*x + 4, (x, 0, 1))

Detail solution

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

$\frac{x \left(2 x^{2} - 15 x + 24\right)}{6}$
Add the constant of integration:

$\frac{x \left(2 x^{2} - 15 x + 24\right)}{6}+ \mathrm{constant}$

The answer is:

$\frac{x \left(2 x^{2} - 15 x + 24\right)}{6}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$${{x^3}\over{3}}-{{5\,x^2}\over{2}}+4\,x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

11/6

$${{11}\over{6}}$$

11/6

$$\frac{11}{6}$$

Simplify

Numerical answer [src]

1.83333333333333

1.83333333333333

The graph

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

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Identical expressions

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Integral of x^2-5x+4 dx

Limits of integration:

The graph:

Piecewise:

The solution