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# Need help with 2 integration problems... watch

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1. Hey guys, Im sorry, I just dont know where to start with these 2 questions...
Any help would be greatly appreciated.

2. For the first one, differentiate the quadratic on the bottom (not the cube bit, just the quadratic) and see if this helps.
3. First one, do substitution. Second one, divide top by bottom and then integrate.

edit: Divide as in polynomial division
4. First one, make a substitution for the bit inside the bracket on the denominator.

Second one, express as a quotient and two partial fractions.
5. for a) make a substitution, then see how the derivative of the substitution relates to the numerator of the fraction

ah... beaten
6. use the substitution
7. (Original post by Mr M)
First one, make a substitution for the bit inside the bracket on the denominator.

Second one, express as a quotient and two partial fractions.
Would it not be easier to do polynomial division on the second one?
8. The first one is very simple because of the derivative of the bottom being a multiple of the top, however the second one requires substitution.
9. (Original post by PeeWeeDan)
The first one is very simple because of the derivative of the bottom being a multiple of the top, however the second one requires substitution.
How's that?
10. (Original post by D-Day)
How's that?
No idea I guessed just from glancing at it. Do I need to give it another looking at?
11. (Original post by D-Day)
Would it not be easier to do polynomial division on the second one?
I don't think so. The remainder would still need some work.

Expressing it in this form sorts it all out in one go.

.
12. (Original post by PeeWeeDan)
No idea I guessed just from glancing at it. Do I need to give it another looking at?
Because top and bottom have the same power, substitution isn't the best method.
13. Too much talk of substitutions for the first one, surely it's quicker to notice

Which is a multiple of the integral you want to do.
14. (Original post by D-Day)
Because top and bottom have the same power, substitution isn't the best method.
Fair enough.
15. (Original post by benwellsday)
Too much talk of substitutions for the first one, surely it's quicker to notice

Which is a multiple of the integral you want to do.
...that's why you do substitution...
16. What? No, from there I would just say

Then you have the answer without integration by substitution. Specifically
17. (Original post by Mr M)
I don't think so. The remainder would still need some work.

Expressing it in this form sorts it all out in one go.

.
How did you get that form? Where do I go from there? How do I find A, B and C? Thanks
18. any help with the 2nd question guys? thanks!
19. Express it in partial fractions. It comes out as the form you just quoted. To find A, B and C you can make it back into a single fraction (by multiplying by the denominators) and then make sure the x^2, x, and constant terms match up for the numerator. The integration is then pretty easy.
20. u cant express 2nd question as a partial fraction becase its a "top havic" which means that the powers of x are same so u cant do that.however i dont know how should u do dat question. I am surethat it cant b expree as partial fraction.

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