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Identical expressions
dx/(x^ three)+cbrt(x)+ one
dx divide by (x cubed ) plus cubic root of (x) plus 1
dx divide by (x to the power of three) plus cubic root of (x) plus one
dx/(x3)+cbrt(x)+1
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Similar expressions
dx/(x^3)-cbrt(x)+1
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Integral of dx/(x^3)+cbrt(x)+1 dx

The solution

You have entered [src]

 oo                    
  /                    
 |                     
 |  /1    3 ___    \   
 |  |-- + \/ x  + 1| dx
 |  | 3            |   
 |  \x             /   
 |                     
/                      
2

$$\int\limits_{2}^{\infty} \left(\left(\sqrt[3]{x} + \frac{1}{x^{3}}\right) + 1\right)\, dx$$

Integral(1/(x^3) + x^(1/3) + 1, (x, 2, oo))

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 $n \neq -1$ :
    
    $\int \sqrt[3]{x}\, dx = \frac{3 x^{\frac{4}{3}}}{4}$
  1. Don't know the steps in finding this integral.
    
    But the integral is
    
    $- \frac{1}{2 x^{2}}$
  The result is: $\frac{3 x^{\frac{4}{3}}}{4} - \frac{1}{2 x^{2}}$
1. The integral of a constant is the constant times the variable of integration:
  
  $\int 1\, dx = x$
The result is: $\frac{3 x^{\frac{4}{3}}}{4} + x - \frac{1}{2 x^{2}}$
Add the constant of integration:

$\frac{3 x^{\frac{4}{3}}}{4} + x - \frac{1}{2 x^{2}}+ \mathrm{constant}$

The answer is:

$\frac{3 x^{\frac{4}{3}}}{4} + x - \frac{1}{2 x^{2}}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

$$\int \left(\left(\sqrt[3]{x} + \frac{1}{x^{3}}\right) + 1\right)\, dx = C + \frac{3 x^{\frac{4}{3}}}{4} + x - \frac{1}{2 x^{2}}$$

Simplify

The answer [src]

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$$\infty$$

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$$\infty$$

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

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Integral of dx/(x^3)+cbrt(x)+1 dx

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Piecewise:

The solution