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Identical expressions
two - three *x^ two + four *x^ three - six *x^- two
2 minus 3 multiply by x squared plus 4 multiply by x cubed minus 6 multiply by x to the power of minus 2
two minus three multiply by x to the power of two plus four multiply by x to the power of three minus six multiply by x to the power of minus two
2-3*x2+4*x3-6*x-2
2-3*x²+4*x³-6*x^-2
2-3*x to the power of 2+4*x to the power of 3-6*x to the power of -2
2-3x^2+4x^3-6x^-2
2-3x2+4x3-6x-2
2-3*x^2+4*x^3-6*x^-2dx
Similar expressions
2-3*x^2-4*x^3-6*x^-2
2+3*x^2+4*x^3-6*x^-2
2-3*x^2+4*x^3+6*x^-2
2-3*x^2+4*x^3-6*x^+2

Integral of 2-3x^2+4x^3-6*x^-2 dx

The solution

You have entered [src]

  1                          
  /                          
 |                           
 |  /       2      3   6 \   
 |  |2 - 3*x  + 4*x  - --| dx
 |  |                   2|   
 |  \                  x /   
 |                           
/                            
0

$$\int\limits_{0}^{1} \left(\left(4 x^{3} + \left(2 - 3 x^{2}\right)\right) - \frac{6}{x^{2}}\right)\, dx$$

Integral(2 - 3*x^2 + 4*x^3 - 6/x^2, (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:
    
    $\int 4 x^{3}\, dx = 4 \int x^{3}\, dx$
    1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
      
      $\int x^{3}\, dx = \frac{x^{4}}{4}$
    So, the result is: $x^{4}$
  1. Integrate term-by-term:
    1. The integral of a constant is the constant times the variable of integration:
      
      $\int 2\, dx = 2 x$
    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: $- x^{3} + 2 x$
  The result is: $x^{4} - x^{3} + 2 x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{6}{x^{2}}\right)\, dx = - 6 \int \frac{1}{x^{2}}\, dx$
  1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \frac{1}{x^{2}}\, dx = - \frac{1}{x}$
  So, the result is: $\frac{6}{x}$
The result is: $x^{4} - x^{3} + 2 x + \frac{6}{x}$
Add the constant of integration:

$x^{4} - x^{3} + 2 x + \frac{6}{x}+ \mathrm{constant}$

The answer is:

$x^{4} - x^{3} + 2 x + \frac{6}{x}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                 
 |                                                  
 | /       2      3   6 \           4    3         6
 | |2 - 3*x  + 4*x  - --| dx = C + x  - x  + 2*x + -
 | |                   2|                          x
 | \                  x /                           
 |                                                  
/

$$\int \left(\left(4 x^{3} + \left(2 - 3 x^{2}\right)\right) - \frac{6}{x^{2}}\right)\, dx = C + x^{4} - x^{3} + 2 x + \frac{6}{x}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$$-\infty$$

-oo

$$-\infty$$

-oo

Numerical answer [src]

-8.27594206769158e+19

-8.27594206769158e+19

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

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Identical expressions

Similar expressions

Integral of 2-3x^2+4x^3-6*x^-2 dx

Limits of integration:

The graph:

Piecewise:

The solution

Other calculators

How to use it?

Identical expressions

Similar expressions

Integral of 2-3*x^2+4*x^3-6*x^-2 dx

Limits of integration:

The graph:

Piecewise:

The solution

Integral of 2-3x^2+4x^3-6*x^-2 dx