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Solving integrals/ dx/(x^3)+cbrt(x)+1

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo                    
  /                    
 |                     
 |  /1    3 ___    \   
 |  |-- + \/ x  + 1| dx
 |  | 3            |   
 |  \x             /   
 |                     
/                      
2
∫2∞((x3+1x3)+1) dx\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

  1. Integrate term-by-term:

    1. Integrate term-by-term:

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x3 dx=3x434\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

        −12x2- \frac{1}{2 x^{2}}

      The result is: 3x434−12x2\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:

      ∫1 dx=x\int 1\, dx = x

    The result is: 3x434+x−12x2\frac{3 x^{\frac{4}{3}}}{4} + x - \frac{1}{2 x^{2}}

  2. Add the constant of integration:

    3x434+x−12x2+constant\frac{3 x^{\frac{4}{3}}}{4} + x - \frac{1}{2 x^{2}}+ \mathrm{constant}

The answer is:

3x434+x−12x2+constant\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          
 |                                            
/
∫((x3+1x3)+1) dx=C+3x434+x−12x2\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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