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lilMissMindset

int. dx/ (x^2 +2x+10) using partial fraction. please.

  • one year ago
  • one year ago

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  1. .Sam.
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    you can't factor that

    • one year ago
  2. .Sam.
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    best approach is to complete the square and then trig substitution

    • one year ago
  3. wasiqss
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    yehh, it will have complex factors

    • one year ago
  4. traile
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    yup

    • one year ago
  5. shivam_bhalla
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    @lilMissMindset To complete the square x^2 +2x+10= x^2+2x+1+9 = (x+1)^2 +3^2 \[\int\limits_{}^{}\frac{dx}{(x+1)^2+3^2}\] Now complete the rest

    • one year ago
  6. shivam_bhalla
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    Remember \[\int\limits_{}^{}\frac{dt}{x^2+a^2} = \frac{1}{a} \tan^{-1}(\frac{x}{a})\]

    • one year ago
  7. shivam_bhalla
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    You can eaily prove the above by substituting x = atan(theta)

    • one year ago
  8. traile
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    @shivam_bhalla she said partial fraction

    • one year ago
  9. TuringTest
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    but it cannot be done with partial fraction if it cannot be factored

    • one year ago
  10. wasiqss
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    traile , it willl become very complex then

    • one year ago
  11. lilMissMindset
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    yeah, im supposed to use that, partial fraction

    • one year ago
  12. shivam_bhalla
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    @LOL, whjy do you want to complicate things when there is a aeasier method available. If you still insist on partial fraction, then it is fine

    • one year ago
  13. wasiqss
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    lil miss it will only have complex factors

    • one year ago
  14. TuringTest
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    there is either a typo, or it's impossible

    • one year ago
  15. shivam_bhalla
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    *why

    • one year ago
  16. TuringTest
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    I mean that using partial fractions is impossible... or at least redundant

    • one year ago
  17. lilMissMindset
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    what am i going to do about this problem then?

    • one year ago
  18. shivam_bhalla
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    Take x+1 = t dx=dt You still get the same thing with partial fractions too

    • one year ago
  19. TuringTest
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    how would you do this with partial fractions? I don't see it... perhaps I am wrong though, it wouldn't be the first time :P

    • one year ago
  20. traile
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    do you think quadratic factors can be use

    • one year ago
  21. shivam_bhalla
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    \[\frac{1}{t^2+9} = \frac{At+B}{t^2+9}\] we see a = 0, B=1 We again get back the same thing. So partail fraction approach should be useless

    • one year ago
  22. shivam_bhalla
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    *partial

    • one year ago
  23. TuringTest
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    like I said then, it's just redundant

    • one year ago
  24. TuringTest
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    by impossible, I meant that the operation is useless, as you just said

    • one year ago
  25. wasiqss
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    you fail turing xD lol jk

    • one year ago
  26. TuringTest
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    @lilMissMindset are you \(sure\) there isn't a typo in your post?

    • one year ago
  27. lilMissMindset
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    yea. im quite sure i typed it right.

    • one year ago
  28. lilMissMindset
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    let's ignore the partial fraction thingy then.

    • one year ago
  29. TuringTest
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    then shivam bhalla has shown you the right way do you know trig substitution integrals?

    • one year ago
  30. lilMissMindset
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    yeah. i'm sorry, i'll do it using trig substitution. thank you so much.

    • one year ago
  31. TuringTest
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    welcome!

    • one year ago
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