Simplifying (x^3)/((x^3)-2): A Guide to Integral Calculations and Complex Roots

  • Thread starter transgalactic
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In summary, the conversation is about finding the integral of (x^3)/((x^3)-2). The speaker divided the polynomials and got 1+ (2/((x^3)-2)). They then tried to split the denominator but encountered complicated roots. They are seeking advice on how to continue after dividing the polynomials, specifically regarding the issue of the exponent being 2 in the denominator instead of 1/3. Another person confirms that the numbers will be ugly and suggests using partial fractions to solve it.
  • #1
transgalactic
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the the integral of

(x^3)/((x^3)-2)

i devided the polinomials and got

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

and afterwards i tried to split the deminator
but i g0t really complicated roots
which are not alowing me to go further
how do i continue after i devided the polinomials
 
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  • #2
nooo

its 2 in the power of(1/3) not 2

thats the big problem
how do i dolve that
 
  • #3
If you want help, type it out w/o ambiguity or use LaTeX to avoid any confusion.
 
  • #4
if we solve ny the formula then we need to substitue eache 2
with 2^(1/3)
 
  • #5
ye Difference of cubes
but you wrote as if it was

x^3 -8


our question is:

1+ (2/((x^3)-2))
 
Last edited:
  • #6
Well after looking at it and confirming with Mathematica, your numbers will be ugly. So you are probably on the right track, and I can't think of a slick way ... I tried several methods but didn't work out nicely at all.
 
  • #7
Lol, I just did it ... it is really ugly in the sense of too many fractions ... I don't even want to type it up. It's pretty ez though, just use Partial Fractions and you're done.
 
  • #8
thanks
 

What is the purpose of simplifying (x^3)/((x^3)-2) in integral calculations?

The purpose of simplifying (x^3)/((x^3)-2) in integral calculations is to make the expression easier to work with and to find the integral of the function. By simplifying, we can identify any complex roots and integrate the function more efficiently.

What are the steps involved in simplifying (x^3)/((x^3)-2)?

The steps involved in simplifying (x^3)/((x^3)-2) are as follows:

  1. Factor out the greatest common factor from the numerator and denominator.
  2. Use algebraic manipulation to simplify the expression.
  3. Identify any complex roots and rewrite the expression in terms of simpler roots.

Why is it important to identify complex roots when simplifying (x^3)/((x^3)-2)?

Identifying complex roots in (x^3)/((x^3)-2) is important because it allows us to rewrite the expression in terms of simpler roots, making it easier to integrate. Additionally, complex roots can help us understand the behavior of the function and its graph.

Can (x^3)/((x^3)-2) be simplified further?

Yes, (x^3)/((x^3)-2) can be simplified further. Depending on the context of the problem, we may be able to further manipulate the expression to make it even simpler. However, it is important to note that simplification ultimately depends on the specific problem at hand.

How can simplifying (x^3)/((x^3)-2) help in solving integrals?

Simplifying (x^3)/((x^3)-2) can help in solving integrals by transforming the expression into a more manageable form. This allows us to use known integration techniques and properties to find the integral of the function. Additionally, simplifying can help us identify any complex roots and make the integration process more efficient.

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