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jotopia34

  • 3 years ago

What is the integral of ln(sqrt t)/t, stuck again!

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  1. tkhunny
    • 3 years ago
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    What have you tried?

  2. jotopia34
    • 3 years ago
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    I will type in what I've done right now

  3. tkhunny
    • 3 years ago
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    Sweet!

  4. amoodarya
    • 3 years ago
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  5. tkhunny
    • 3 years ago
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    ?? Is that the same problem?

  6. jotopia34
    • 3 years ago
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    \[u=\sqrt{t}\] du= 1/2 t^-1/2 dt du=1/2*1/sqr(t) dt But I know its wrong because I still can't cancel anything

  7. amoodarya
    • 3 years ago
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    i think it was integral ln sqrt x dx isnt it ? or it is int ln(sqrtx)/x dx ?

  8. tkhunny
    • 3 years ago
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    Why would you use a square root substitution when you can use a logarithm property?

  9. slaaibak
    • 3 years ago
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    yeah.. ln(sqrt(t)) = 1/2 ln t

  10. jotopia34
    • 3 years ago
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    what is that property again please? in general format?

  11. slaaibak
    • 3 years ago
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    \[\ln(x^a) = a \times \ln(x)\]

  12. jotopia34
    • 3 years ago
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    ohhhh, now I see, the square root is 1/2 as exponent. Thus, that is my (a). Thank u!!

  13. slaaibak
    • 3 years ago
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    Cool :) do you know how to go from here?

  14. jotopia34
    • 3 years ago
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    yes, I believe so

  15. slaaibak
    • 3 years ago
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    shot

  16. jotopia34
    • 3 years ago
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    is the answer 1/4 * (lnx)^2+C? I think its wrong. I saw a post from another guy and I don't get what he wrote. Slaaibak, you make excellent sense. Can you post the solution steps? Id be eternally grateful...

  17. amoodarya
    • 3 years ago
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  18. jotopia34
    • 3 years ago
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    Amoodarya, your last posting is the final answer I got, so I think I got it right....

  19. slaaibak
    • 3 years ago
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    Sure. \[\int\limits {1 \over 2} {\ln t \over t} dt\] Let's set k = ln t dk = 1/t dt so the integral becomes; \[{1 \over 2} \int\limits k dk = {1 \over 4 }k^2 + C = {1 \over 4}(\ln t)^2 + C\]

  20. jotopia34
    • 3 years ago
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    yes!! You are all geniuses!

  21. slaaibak
    • 3 years ago
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    haha, if only :( hope it helped. thank you for the fun, makes insomnia a bit better.

  22. jotopia34
    • 3 years ago
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    insomia is the curse of genius

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