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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

(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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,249

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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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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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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,426

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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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,249

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

Hi!

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!

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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