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Identical expressions
(x^ three - two x^2+x+ three)
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x3-2x2+x+3
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x^3-2x^2+x+3
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Similar expressions
(x^3-2x^2+x-3)
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Solving integrals/ (x^3-2x^2+x+3)

Integral of (x^3-2x^2+x+3) dx

The solution

You have entered [src]

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

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

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

Detail solution

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

$\frac{x \left(3 x^{3} - 8 x^{2} + 6 x + 36\right)}{12}$
Add the constant of integration:

$\frac{x \left(3 x^{3} - 8 x^{2} + 6 x + 36\right)}{12}+ \mathrm{constant}$

The answer is:

$\frac{x \left(3 x^{3} - 8 x^{2} + 6 x + 36\right)}{12}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

292/3

$${{292}\over{3}}$$

292/3

$$\frac{292}{3}$$

Simplify

Numerical answer [src]

97.3333333333333

97.3333333333333

The graph

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

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Integral of (x^3-2x^2+x+3) dx

Limits of integration:

The graph:

Piecewise:

The solution