Question

how to do the fraction decomposition of:
(4n^2 + n)/(n^7 +n^3)^1/3

Answer 1

\[\frac {4n^2 + n} { \sqrt[3]{{n^7 +n^3}}} \rightarrow \frac {n(4n + 1)} {n \sqrt[3]{{n^4 +1}}} = \frac {4n + 1}{\sqrt[3]{{n^4 +1}}}\]Thats a start I guess.

Answer 2

I would do something like

x = (4n^2+n)/(n^7+n^3)^(1/3) (Assuming you mean a cube root, not divide by 3)

From there

x^3 = (4n^2+n)^3/(n^7+n^3)

And then you can solve for that partial fraction decomposition and then cube root it in the end, but that might get ugly. I'm not sure, but there might be a more elegant solution.

Answer 3

i am still lost :|

Answer 4

Is this in an integral, or is it the actual question?

Answer 5

The Answer Is (Simplified) 4n^2+n over (n^7+n^3)^1 over 3

Answer 6

\[u = \sqrt[3]{{n^4 +1}}, u^3 = n^4 + 1, n = \sqrt[4]{u^3 - 1}\]\[\frac {4n + 1}{\sqrt[3]{{n^4 +1}}} \rightarrow \frac {4 \sqrt[4]{u^3 - 1} + 1}{u} \rightarrow \frac {4 \sqrt[4]{u^3 - 1}}{u} + \frac {1}{u}\]Which gets to nowhere... :(

Answer 7

The answer is this mess...