A community for students.
Here's the question you clicked on:
 0 viewing
RolyPoly
 2 years ago
<Integration>
\[\frac{1}{5}\int \frac{x^3+2x^23x+4}{x^4x^3+x^2x+1}dx\]
RolyPoly
 2 years ago
<Integration> \[\frac{1}{5}\int \frac{x^3+2x^23x+4}{x^4x^3+x^2x+1}dx\]

This Question is Closed

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0@hartnn If you don't mind giving a hand here...

hobbs
 2 years ago
Best ResponseYou've already chosen the best response.0@RolyPoly Man i'm sorry but i can't find the answer... ive been tryin for the past 20 mins

SithsAndGiggles
 2 years ago
Best ResponseYou've already chosen the best response.0I'd suggest partial fractions, but I don't know if that'd get you anywhere with this one.

hobbs
 2 years ago
Best ResponseYou've already chosen the best response.0@SithsAndGiggles i tried but just got a mess

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0Where there's a will, there's a way! :D

FoolAroundMath
 2 years ago
Best ResponseYou've already chosen the best response.0\(\text{Denominator = } 1x+x^2x^3+x^4 = (1+x^5)/(1+x)\) \[ \implies \frac{1}{5}\int\frac{5(1x+x^2x^3+x^4)}{x^5+1}dx=\int\frac{1}{5(x+1)}+\frac{1}{x^5+1}dx\] Hope this helps

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0The problem is I get this integral from \(\int \frac{1}{x^5+1}dx\)... \[\int \frac{1}{x^5+1}dx=\int ( \frac{1}{5(x+1)} + \frac{(x^3 + 2x^2  3x + 4)}{5(x^4x^3+x^2x+1)})dx\]

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0If you change it back to \(\int \frac{1}{x^5+1}dx\), then, how can I solve this integral?

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3not real sure how this would help, but this is an idea im trying to play with \[\frac{\sum_{0}^{4}(1)^n(4n)x^n}{\sum_{0}^{4}(1)^n~5~x^n}\] \[\frac{\sum_{0}^{4}(1)^n4~x^n\sum_{0}^{4}n~x^n}{\sum_{0}^{4}(1)^n~5~x^n}\] \[\frac{\sum_{0}^{4}(1)^n4~x^n}{\sum_{0}^{4}(1)^n~5~x^n}\frac{\sum_{0}^{4}n~x^n}{\sum_{0}^{4}(1)^n~5~x^n}\]

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3when I simply do the division, i get a series representation of:\[\sum_0~(1)^n(4x^{5n}+x^{5n+1}x^{5n+2}+x^{5n+3}x^{5n+4})\]

SithsAndGiggles
 2 years ago
Best ResponseYou've already chosen the best response.0@amistre64, I like your idea of using the pattern of coefficients. I also don't know if it helps, but I like the idea nonetheless.

amistre64
 2 years ago
Best ResponseYou've already chosen the best response.3thnx, its was either that or try to figure out what the wolf did :) http://www.wolframalpha.com/input/?i=integrate+%2843x%2B2x%5E2x%29%2F%285%281x%2Bx%5E2x%5E3%2Bx%5E4%29%29+dx I recall hearing that a power series solution is a solution; and if its an important enough solution, they give it a name ;)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0lol forget it http://www.wolframalpha.com/input/?i= \frac{1}{5}\int+\frac{x^3%2B2x^23x%2B4}{x^4x^3%2Bx^2x%2B1}dx

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0\[\frac{\sum_{0}^{4}(1)^n(4n)x^n}{\sum_{0}^{4}(1)^n~5~x^n}\]\[=\frac{\sum_{0}^{4}(1)^n(4)x^n(1)^nnx^n}{\sum_{0}^{4}(1)^n~5~x^n}\]Is this step correct?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0i am not sure you are going to find a nice closed form for this you can integrate term by term if you expand \(\frac{1}{1+x^5}\) as a power series start with \[\frac{1}{1+x}=1x+x^2x^3+...\] and then replace \(x\) by \(x^5\) and get \[\frac{1}{1+x^5}=1x^5+x^{10}...\] and i guess you can integrate that term by term

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0gives \[x\frac{x^6}{6}+\frac{x^{11}}{11}...\]

RolyPoly
 2 years ago
Best ResponseYou've already chosen the best response.0Hmm... Is \[\frac{\sum_{0}^{4}(1)^n(4n)x^n}{\sum_{0}^{4}(1)^n~5~x^n}=\frac{\sum_{0}^{4}(1)^n(4)x^n(1)^nnx^n}{\sum_{0}^{4}(1)^n~5~x^n}\]correct?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.