## anonymous one year ago My achilles heel....

1. anonymous

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2. anonymous

These types of integrals have always been hard, Id appreciate any step by step explanation :)

3. IrishBoy123

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4. IrishBoy123

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5. UsukiDoll

ah long division. because the exponent in the denominator is higher than the one int he numerator.

6. anonymous

Usuki!! :)

7. UsukiDoll

do you know long division?

8. anonymous

kind of, I think I do.

9. UsukiDoll

I have faith in you . you can do it ;)

10. imqwerty

^ :D

11. anonymous

Im afraid faith cant save u or me...help:)?

12. UsukiDoll

@imqwerty is a good helper. He will guide you ! :D

13. anonymous

bhaiya help?

14. imqwerty

•_•)

15. anonymous

haha dont we all have to do that :)

16. anonymous

Back to my problem yaar...I got the last exam in calc 2 ever given in sweden, no chance to fail this.

17. anonymous

Guys....my problem?

18. IrishBoy123

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19. IrishBoy123

finish it off now?

20. UsukiDoll

don't we have to switch signs for polynomial long division though?

21. imqwerty

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22. UsukiDoll

how the....... O_O @imqwerty what did you do?

23. imqwerty

:D

24. anonymous

Guys those methods u showed I dont know them....

25. imqwerty

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26. nincompoop

he used factorization to break the denominator

27. UsukiDoll

what! everyone should know long division by now. as for those separate integrals.. I see log and arctan

28. UsukiDoll

I know that we can use factorization on the denominator to get x (x^2+1) . I'm talking about the numerator part. @imqwerty got it uber fast.

29. anonymous

alright go on imqwerty.

30. UsukiDoll

I'm 94 SS NOW! XD!

31. nincompoop

that is not how you properly break the sum of terms with denominator although they yield the same quotient

32. imqwerty

i broke the equation into 2 parts nd spiltted them nd now we get a cute thing which can be solved easily :)

33. UsukiDoll

. We know that the exponent in the denominator is huge than the one in the numerator so we need to use long division to fix this problem

34. anonymous

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35. anonymous

but @imqwerty what happened to 2x^2+x+2?

36. UsukiDoll

that's what I'm wondering too... for the numerator.

37. imqwerty

did u get how i broke the equation??

38. UsukiDoll

I got the steps after the equation got broken up

39. anonymous

could u break the equation, thats the only unclear part. otherwise it was very fast and welldone.

40. nincompoop

I get how you did it but we do not know how the terms are properly constructed to yield the sum of terms I do not think that is mathematically sound: $$\large \frac{2x^2}{x^3+x}+\frac{x}{x^3+x}+\frac{2}{x^3+x} \rightarrow \frac{2x^3}{x(x^2+1)}...$$

41. IrishBoy123

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42. imqwerty

try takin LCM of those those to terms nd u'll see the original equation appears ok in such questions in which both the numerator and denominator have x our strategy shuld be to break the equation into parts so that all the x terms vanish frm the numerator

43. IrishBoy123

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44. imqwerty

now what i did = (2x^2 + x +2)/(x^3 + x) =2/x + 1/(x^2+1) if u solve this^ then we get ------> [2(x^2+1) + x]/[x(x^2+1)] =(2x^2 + x+2)/(x^3+x) we did nothin wrng we jst altered the equation so as to make it easy to differentiate :)

45. nincompoop

clever I must say

46. imqwerty

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47. imqwerty

:D

48. IrishBoy123

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49. imqwerty

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50. IrishBoy123

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51. anonymous

thnx, this wasnt easy I must say.