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amorfide

  • 3 years ago

integrate 1/3x+2

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  1. amorfide
    • 3 years ago
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    |dw:1350485381398:dw|

  2. amorfide
    • 3 years ago
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    is this right?

  3. amorfide
    • 3 years ago
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    @ParthKohli

  4. Zarkon
    • 3 years ago
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    +c

  5. amorfide
    • 3 years ago
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    that stupid freaking C lol

  6. ParthKohli
    • 3 years ago
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    Yeah, that is and then a constant... don't forget the constant.

  7. amorfide
    • 3 years ago
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    parth tell me how to integrate this one...

  8. amorfide
    • 3 years ago
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    |dw:1350485522236:dw|

  9. ParthKohli
    • 3 years ago
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    \[2\int{dx \over x^2 + 3}\]That's tricky stuff: trig substitution.

  10. amorfide
    • 3 years ago
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    i literally cant do it :P

  11. ParthKohli
    • 3 years ago
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    no no no... wait

  12. ParthKohli
    • 3 years ago
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    not trig substitution

  13. amorfide
    • 3 years ago
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    if it was 2/x²+1 it would be a trig function

  14. ParthKohli
    • 3 years ago
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    @Zarkon Please, if you might be able to help?

  15. Zarkon
    • 3 years ago
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    you can use trig sub

  16. ParthKohli
    • 3 years ago
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    Got it

  17. ParthKohli
    • 3 years ago
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    How?

  18. Zarkon
    • 3 years ago
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    \[x=\sqrt{3}\tan(\theta)\]

  19. amorfide
    • 3 years ago
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    huh explain?

  20. ParthKohli
    • 3 years ago
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    Oh, yup...that makes sense.

  21. ParthKohli
    • 3 years ago
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    @amorfide Trigonometric substitution! Search it on Google.

  22. Zarkon
    • 3 years ago
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    if you have \[\int\frac{2}{x^2+1}dx\] then just recall that \(\displaystyle\frac{d}{dx}\tan^{-1}(x)=\frac{1}{x^2+1}\) and therefore \[\int\frac{2}{x^2+1}dx=2\cdot\tan^{-1}(x)+c\] if you want \[\int\frac{2}{x^2+3}dx\] then, if you want, you can use the substitution I gave above

  23. amorfide
    • 3 years ago
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    so if 2/(x²+1) = 2tan^-1(x/root1) all over root 1 2/(x²+3) = |dw:1350487017539:dw|

  24. Zarkon
    • 3 years ago
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    +c ;)

  25. amorfide
    • 3 years ago
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    LOL thank you! always forget the C... would i lose a mark for not putting +c if i do not need to figure out C?

  26. Zarkon
    • 3 years ago
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    yes

  27. amorfide
    • 3 years ago
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    ahh okay, thank you :D

  28. Zarkon
    • 3 years ago
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    there will be a time in the future when you will find a value for C. Particularly when doing initial value differential equations

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