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Identical expressions
(two x^ three -sqrt(four)+ four)/(x^2)
(2x cubed minus square root of (4) plus 4) divide by (x squared )
(two x to the power of three minus square root of (four) plus four) divide by (x squared )
(2x^3-√(4)+4)/(x^2)
(2x3-sqrt(4)+4)/(x2)
2x3-sqrt4+4/x2
(2x³-sqrt(4)+4)/(x²)
(2x to the power of 3-sqrt(4)+4)/(x to the power of 2)
2x^3-sqrt4+4/x^2
(2x^3-sqrt(4)+4) divide by (x^2)
(2x^3-sqrt(4)+4)/(x^2)dx
Similar expressions
(2x^3-sqrt(4)-4)/(x^2)
(2x^3+sqrt(4)+4)/(x^2)

Solving integrals/ (2x^3-sqrt(4)+4)/(x^2)

Integral of (2x^3-sqrt(4)+4)/(x^2) dx

The solution

You have entered [src]

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

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

Integral((2*x^3 - sqrt(4) + 4)/x^2, (x, 0, 1))

Detail solution

Rewrite the integrand:

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

$\frac{x^{3} - 2}{x}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

2.75864735589719e+19

2.75864735589719e+19

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

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Integral of (2x^3-sqrt(4)+4)/(x^2) dx

Limits of integration:

The graph:

Piecewise:

The solution