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#1 2012-11-28 20:56:22

jacks
Member
Registered: 2012-11-21
Posts: 80

Indefinite integration

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#2 2012-11-28 21:00:08

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,465

Re: Indefinite integration

(x + 1) is a factor of top and bottom.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2012-11-28 21:15:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,517

Re: Indefinite integration

Hi jacks;

The answer for that is huge, are you supposed to do that by hand?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#4 2012-11-29 01:46:46

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,596

Re: Indefinite integration

bob bundy wrote:

(x + 1) is a factor of top and bottom.

Bob

It is not.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2012-11-29 03:19:20

Agnishom
Real Member
From: The Complex Plane
Registered: 2011-01-29
Posts: 17,903
Website

Re: Indefinite integration

It is a factor of the denominator only.


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'You have made another human being happy. There is no greater accomplishment.' -bobbym

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#6 2012-11-29 04:26:55

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,465

Re: Indefinite integration

Sorry, you are right.  Selective blindness again.

I was having trouble with my minus signs. 

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#7 2012-11-29 06:29:25

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,596

Re: Indefinite integration

The integral can be solved through partial fractions, but it is a nasty factorisation!


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#8 2012-11-29 09:20:54

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,517

Re: Indefinite integration

Hi;

Yes, it looks like a handmade one. That can be dangerous.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#9 2012-11-29 15:38:17

noelevans
Member
Registered: 2012-07-20
Posts: 236

Re: Indefinite integration

Hi! smile

The third degree polynomial divided by the fifth degree polynomial can be written as an infinite
series as:

Then just integrate it term by term to get the indefinite integral in an infinite series form.

Starting with the 1/x^2 term the coefficients in the series repeat in blocks of 10 in the pattern
1,-1,1,0,0,-1,1,-1,0,0.  That is what the 1/(x^10n) handles.  So the next 6 terms in the series
would have exponents on the bottom of 12,13,14,17,18,19 and the next 6 would have
22,23,24,27,28,29 for the exponents on the bottom.

The signs in each block of six terms would continue to be 1, -1, 1, -1, 1, -1.

Has anyone got a closed form for the integral?  I'd love to see it.  If x^5+1 is divided by x-1 I get
x(x+1)(x-1)(x^2+1)  +  (x+1)/(x-1)  but I haven't been able to use this to get a closed form.

Good luck with it! dizzy


Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

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