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

The solution

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

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

Integral(x^2 - 4*x + 5, (x, 1, 3))

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

$\frac{x \left(x^{2} - 6 x + 15\right)}{3}$
Add the constant of integration:

$\frac{x \left(x^{2} - 6 x + 15\right)}{3}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{2} - 6 x + 15\right)}{3}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

8/3

$${{8}\over{3}}$$

8/3

$$\frac{8}{3}$$

Упростить

Numerical answer [src]

2.66666666666667

2.66666666666667

The graph

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

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

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The solution