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# Integrating a fraction

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1. How would you integrate

2x^2/(1+x) ?

Attempted to use partial fractions but not successful ?
2. (Original post by jon2016)
How would you integrate

2x^2/(1+x) ?

Attempted to use partial fractions but not successful ?
Long division. You should get then long division on the second fraction as well.
3. substitution?

u=1+x
4. How exactly would long division work with polynomials ? The X in the numerator cant cancel out ?

(Original post by Zacken)
Long division. You should get then long division on the second fraction as well.
The textbook does this http://imgur.com/a/ABxPl

Not sure what method they followed ?
5. (Original post by jon2016)
How exactly would long division work with polynomials ? The X in the numerator cant cancel out ?

The textbook does this http://imgur.com/a/ABxPl

Not sure what method they followed ?
What they've done is

No perform the same 'trick' or 'technique' on the second fraction by
6. (Original post by Zacken)
What they've done is

No perform the same 'trick' or 'technique' on the second fraction by
wow thats amazing, I would never have thought of doing that in the exam ! thanks so much.

Out of curiosity, are there any clear things to look for , so you know which integration technique to use ? from partial, sub and by parts ?
7. (Original post by jon2016)
wow thats amazing, I would never have thought of doing that in the exam ! thanks so much.

Out of curiosity, are there any clear things to look for , so you know which integration technique to use ? from partial, sub and by parts ?
The thing is, here - long division and substitution would have worked as well as just this basic simplification. You might want to learn "long division for polynomials" so you're able to do what I did in my previous post but without it requiring any creative thought and it's a lot more systematic.

You tend to get used to what technique to use once you've done enough practice; normally IBP is when you have a product of two functions where each is easy integrable/differentiable but put together they aren't, etc...
8. (Original post by Zacken)
The thing is, here - long division and substitution would have worked as well as just this basic simplification. You might want to learn "long division for polynomials" so you're able to do what I did in my previous post but without it requiring any creative thought and it's a lot more systematic.

You tend to get used to what technique to use once you've done enough practice; normally IBP is when you have a product of two functions where each is easy integrable/differentiable but put together they aren't, etc...
Could we have used partial fractions for the above question ?
9. (Original post by jon2016)
Could we have used partial fractions for the above question ?
Well, no - you can only use partial fractions when there is more than one factor in the denominator. But all you have here is in the denominator, which you can't do anything with, unfortunately.
10. (Original post by Zacken)
Well, no - you can only use partial fractions when there is more than one factor in the denominator. But all you have here is in the denominator, which you can't do anything with, unfortunately.
what about e^ root(x) / root(x)

My textbook does it by Integration by substitution, but the fact is has two terms, suggested to me it should be Integration by parts ?
11. (Original post by jon2016)
what about e^ root(x) / root(x)

My textbook does it by Integration by substitution, but the fact is has two terms, suggested to me it should be Integration by parts ?
You can do it by parts, if you want: .

And .

And that would work out fine.
12. (Original post by Zacken)
You can do it by parts, if you want: .

And .

And that would work out fine.
ah right thanks, it didnt occur to me

Is this a legitimate maths rearranging technique http://i.imgur.com/i1kWglN.jpg ie multpiply numerator and denominator by 2
13. (Original post by jon2016)

Is this a legitimate maths rearranging technique http://i.imgur.com/i1kWglN.jpg ie multpiply numerator and denominator by 2
Very much so! You learnt about this technique in middle school, I'm sure. How do you add . Well, you take the and multiplied the numerator and denominator by to get . So that you could write .

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