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Identical expressions
(x³+ three x²-2x+3)
(x³ plus 3x² minus 2x plus 3)
(x³ plus three x² minus 2x plus 3)
x³+3x²-2x+3
(x³+3x²-2x+3)dx
Similar expressions
(x³-3x²-2x+3)
(x³+3x²-2x-3)
(x³+3x²+2x+3)

Integral of (x³+3x²-2x+3) dx

The solution

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

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

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

$x \left(\frac{x^{3}}{4} + x^{2} - x + 3\right)$
Add the constant of integration:

$x \left(\frac{x^{3}}{4} + x^{2} - x + 3\right)+ \mathrm{constant}$

The answer is:

$x \left(\frac{x^{3}}{4} + x^{2} - x + 3\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \left(\left(- 2 x + \left(x^{3} + 3 x^{2}\right)\right) + 3\right)\, dx = C + \frac{x^{4}}{4} + x^{3} - x^{2} + 3 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

13/4

$$\frac{13}{4}$$

13/4

$$\frac{13}{4}$$

13/4

Numerical answer [src]

3.25

3.25

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

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Identical expressions

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Integral of (x³+3x²-2x+3) dx

Limits of integration:

The graph:

Piecewise:

The solution