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dx/x³(1+x⁴)²

Integral of dx/x³(1+x⁴)² dx

Limits of integration:

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The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo             
  /             
 |              
 |          2   
 |  /     4\    
 |  \1 + x /    
 |  --------- dx
 |       3      
 |      x       
 |              
/               
2               
$$\int\limits_{2}^{\infty} \frac{\left(x^{4} + 1\right)^{2}}{x^{3}}\, dx$$
Integral((1 + x^4)^2/x^3, (x, 2, oo))
Detail solution
  1. There are multiple ways to do this integral.

    Method #1

    1. Rewrite the integrand:

    2. Integrate term-by-term:

      1. The integral of is when :

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. The integral of is when :

        So, the result is:

      1. The integral of is when :

      The result is:

    Method #2

    1. Rewrite the integrand:

    2. Let .

      Then let and substitute :

      1. The integral of a constant times a function is the constant times the integral of the function:

        1. Rewrite the integrand:

        2. Integrate term-by-term:

          1. The integral of is when :

          1. The integral of a constant is the constant times the variable of integration:

          1. The integral of is when :

          The result is:

        So, the result is:

      Now substitute back in:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                 
 |                                  
 |         2                        
 | /     4\                        6
 | \1 + x /            2    1     x 
 | --------- dx = C + x  - ---- + --
 |      3                     2   6 
 |     x                   2*x      
 |                                  
/                                   
$$\int \frac{\left(x^{4} + 1\right)^{2}}{x^{3}}\, dx = C + \frac{x^{6}}{6} + x^{2} - \frac{1}{2 x^{2}}$$
The graph
The answer [src]
oo
$$\infty$$
=
=
oo
$$\infty$$
oo
The graph
Integral of dx/x³(1+x⁴)² dx

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