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

jacks
Member
Registered: 2012-11-21
Posts: 132

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

bob bundy
Registered: 2010-06-20
Posts: 8,371

### Re: Indefinite integration

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

Bob

Children are not defined by school ...........The Fonz
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
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
The knowledge of some things as a function of age is a delta function.

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

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,856
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'
I'm not crazy, my mother had me tested.

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

bob bundy
Registered: 2010-06-20
Posts: 8,371

### Re: Indefinite integration

Sorry, you are right.  Selective blindness again.

I was having trouble with my minus signs.

Bob

Children are not defined by school ...........The Fonz
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: Harlan's World
Registered: 2011-05-23
Posts: 16,037

### 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
The knowledge of some things as a function of age is a delta function.

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

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### 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.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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

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

### Re: Indefinite integration

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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## #10 2017-10-27 21:01:14

santner
Member
Registered: 2017-10-27
Posts: 2

### Re: Indefinite integration

You have to do by partial fraction.
Check Integration Formulas here

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