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

[transgalactic]

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

 

[transgalactic]

nooo

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

thats the big problem
how do i dolve that

 

[rocomath]

If you want help, type it out w/o ambiguity or use LaTeX to avoid any confusion.

 

[transgalactic]

if we solve ny the formula then we need to substitue eache 2
with 2^(1/3)

 

[transgalactic]

ye Difference of cubes
but you wrote as if it was

x^3 -8


our question is:

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

 

[rocomath]

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.

 

[rocomath]

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.

 

[transgalactic]

thanks