Mister Exam

Lang:

Other calculators

How to use it?
Integral of d{x}:
Integral of sqrt(x)/x
Integral of (x^2-1)e^x
Integral of sqrt(x^2+4)
Integral of x^3/(x^2+1)^2
Graphing y =:
x^3-3x-2
Identical expressions
x^ three -3x- two
x cubed minus 3x minus 2
x to the power of three minus 3x minus two
x3-3x-2
x³-3x-2
x to the power of 3-3x-2
x^3-3x-2dx
Similar expressions
x^3+3x-2
x^3-3x+2

Integral of x^3-3x-2 dx

The solution

You have entered [src]

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

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

Integral(x^3 - 3*x - 2, (x, 0, 1))

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

$\frac{x \left(x^{3} - 6 x - 8\right)}{4}$
Add the constant of integration:

$\frac{x \left(x^{3} - 6 x - 8\right)}{4}+ \mathrm{constant}$

The answer is:

$\frac{x \left(x^{3} - 6 x - 8\right)}{4}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

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.

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of x^3-3x-2 dx

Limits of integration:

The graph:

Piecewise:

The solution