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anonymous

  • 5 years ago

evaluate the definite integral.... from 1 to e^4 dx/(x(1+ln(x)))

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  1. anonymous
    • 5 years ago
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    Note d/dx (ln(x)) = 1/(x) and do it from inspection.

  2. anonymous
    • 5 years ago
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    Or if you're a baby, let u = ln(x)

  3. anonymous
    • 5 years ago
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    \[\int_1^{e^4} \frac{1}{x(1+1ln(x))} dx\] \(\text{Let u} = ln(x) \implies du = \frac{1}{x}dx \implies dx = x\ du\)

  4. anonymous
    • 5 years ago
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    Or if you're a douche you can learn all this stuff before hand then come online and make fun of other people who don't know how to do it yet.

  5. anonymous
    • 5 years ago
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    whats the final answer? i'm confused

  6. anonymous
    • 5 years ago
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    Did you try it with the u substitution I suggested?

  7. anonymous
    • 5 years ago
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    tryin now

  8. anonymous
    • 5 years ago
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    r u left with 1/u?

  9. anonymous
    • 5 years ago
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    \(\frac{1}{1+u}\)

  10. anonymous
    • 5 years ago
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    Actually a better u sub might be let u = 1+lnx

  11. anonymous
    • 5 years ago
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    Then you'll get 1/u

  12. anonymous
    • 5 years ago
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    Honestly, polpak, I know you hate me, but if you can't see this is clearly a case to use: \[\int\limits \frac{f'(x)}{f(x)} \mathbb{d}x = f(x) + c\] you are silly. Ah well, I guess less intelligent people who learn maths by rote always fall back on subs. ..

  13. anonymous
    • 5 years ago
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    ln f(x) = the result, my bad

  14. anonymous
    • 5 years ago
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    so then how would i integrate 1/u? is it ln(u)?

  15. anonymous
    • 5 years ago
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    It's not a matter of whether or not I can see it. It's a matter of someone learning it for the first time needs to understand a bit about the process and how to do things even when it's somthing not so nice. And to do that, they have to first practice on nice things.

  16. anonymous
    • 5 years ago
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    Newton, nobody cares if you can do it. This is a place for helping others learn, not for trying to impress people by being awsome at math.

  17. anonymous
    • 5 years ago
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    Cambridge Part III Tripos would eat you alive, kiddo (polpak)

  18. anonymous
    • 5 years ago
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    Let −90f(x)dx=5 −9−6f(x)dx=7 −30f(x)dx=4 . Find −6−3f(x)dx= and −3−6(5f(x)−7)dx=

  19. anonymous
    • 5 years ago
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    sorry that didnt copy right

  20. anonymous
    • 5 years ago
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    Polpak, I told him both ways to do it faster than you LaTeX'd one, and you're bitter. grow up.

  21. anonymous
    • 5 years ago
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    I'm not bitter. I wouldn't have had a problem if you'd given him(her?) helpful advice, and then went on to explain how to do it easier. But to give a trite one line explanation and then tell him(her?) to do it by inspection is just you showing off, not trying to help. Then you go on to give him(her?) a way he might understand, while simultaneously insulting him(her?). You're just being an retriceat, and you've been at it all day. How about you go find the Cambridge math club and have yourself a nice circlejerk.

  22. anonymous
    • 5 years ago
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    I was taught to integrate things of that form by inspection. Maybe I shouldn't assume everyone was (though they should be) - and that is long before University, it is how it is taught to everyone who does Maths in England. Substitutions waste time.

  23. anonymous
    • 5 years ago
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    poketjjax: did you get it solved?

  24. anonymous
    • 5 years ago
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    yes i did. i have another one as well.

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