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Graphing y =:
x^3-3x^2+5
Equation:
x^3-3x^2+5
Identical expressions
x^ three -3x^ two + five
x cubed minus 3x squared plus 5
x to the power of three minus 3x to the power of two plus five
x3-3x2+5
x³-3x²+5
x to the power of 3-3x to the power of 2+5
x^3-3x^2+5dx
Similar expressions
x^3-3x^2-5
x^3+3x^2+5

Integral of x^3-3x^2+5 dx

The solution

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

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

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

Detail solution

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

$x \left(\frac{x^{3}}{4} - x^{2} + 5\right)$
Add the constant of integration:

$x \left(\frac{x^{3}}{4} - x^{2} + 5\right)+ \mathrm{constant}$

The answer is:

$x \left(\frac{x^{3}}{4} - x^{2} + 5\right)+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \left(\left(x^{3} - 3 x^{2}\right) + 5\right)\, dx = C + \frac{x^{4}}{4} - x^{3} + 5 x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$4$$

Numerical answer [src]

4.0

4.0

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

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Integral of x^3-3x^2+5 dx

Limits of integration:

The graph:

Piecewise:

The solution