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Derivative of:
x^3-3x^2+1
Graphing y =:
x^3-3x^2+1
Identical expressions
x^ three -3x^ two + one
x cubed minus 3x squared plus 1
x to the power of three minus 3x to the power of two plus one
x3-3x2+1
x³-3x²+1
x to the power of 3-3x to the power of 2+1
x^3-3x^2+1dx
Similar expressions
x^3+3x^2+1
x^3-3x^2-1

Solving integrals/ x^3-3x^2+1

Integral of x^3-3x^2+1 dx

The solution

You have entered [src]

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

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

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

Detail solution

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

$\frac{x^{4}}{4} - x^{3} + x+ \mathrm{constant}$

The answer is:

$\frac{x^{4}}{4} - x^{3} + x+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                    
 |                                    4
 | / 3      2    \               3   x 
 | \x  - 3*x  + 1/ dx = C + x - x  + --
 |                                   4 
/

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$0$$

Упростить

Numerical answer [src]

5.62837573394741e-19

5.62837573394741e-19

The graph

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

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Integral of x^3-3x^2+1 dx

Limits of integration:

The graph:

Piecewise:

The solution