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Identical expressions
x^(- two / three)- two /x^ three + one
x to the power of ( minus 2 divide by 3) minus 2 divide by x cubed plus 1
x to the power of ( minus two divide by three) minus two divide by x to the power of three plus one
x(-2/3)-2/x3+1
x-2/3-2/x3+1
x^(-2/3)-2/x³+1
x to the power of (-2/3)-2/x to the power of 3+1
x^-2/3-2/x^3+1
x^(-2 divide by 3)-2 divide by x^3+1
x^(-2/3)-2/x^3+1dx
Similar expressions
x^(-2/3)+2/x^3+1
x^(-2/3)-2/x^3-1
x^(2/3)-2/x^3+1

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

Integral of x^(-2/3)-2/x^3+1 dx

The solution

You have entered [src]

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

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

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

Detail solution

Integrate term-by-term:
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \left(- \frac{2}{x^{3}}\right)\, dx = - \int \frac{2}{x^{3}}\, dx$
  1. The integral of a constant times a function is the constant times the integral of the function:
    
    $\int \frac{2}{x^{3}}\, dx = 2 \int \frac{1}{x^{3}}\, dx$
    1. Don't know the steps in finding this integral.
      
      But the integral is
      
      $- \frac{1}{2 x^{2}}$
    So, the result is: $- \frac{1}{x^{2}}$
  So, the result is: $\frac{1}{x^{2}}$
1. The integral of $x^{n}$ is $\frac{x^{n + 1}}{n + 1}$ when $n \neq -1$ :
  
  $\int \frac{1}{x^{\frac{2}{3}}}\, dx = 3 \sqrt[3]{x}$
The result is: $3 \sqrt[3]{x} + x + \frac{1}{x^{2}}$
Add the constant of integration:

$3 \sqrt[3]{x} + x + \frac{1}{x^{2}}+ \mathrm{constant}$

The answer is:

$3 \sqrt[3]{x} + x + \frac{1}{x^{2}}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$x+3\,x^{{{1}\over{3}}}+{{1}\over{x^2}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

-oo

$${\it \%a}$$

-oo

$$-\infty$$

Simplify

Numerical answer [src]

-1.83073007580698e+38

-1.83073007580698e+38

The graph

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

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Identical expressions

Similar expressions

Integral of x^(-2/3)-2/x^3+1 dx

Limits of integration:

The graph:

Piecewise:

The solution