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geerky42

  • 3 years ago

\[\Large \int \dfrac{dx}{\ln x}\]

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  1. inkyvoyd
    • 3 years ago
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    set u=ln x then du/dx/u

  2. inkyvoyd
    • 3 years ago
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    you should be able to figure it out with u-sub

  3. geerky42
    • 3 years ago
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    du/dx/u?

  4. geerky42
    • 3 years ago
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    but then how can I use du? There is no place to put du

  5. inkyvoyd
    • 3 years ago
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    I may have overlooked this >.< gimme a minute getting some paper

  6. Kanwar245
    • 3 years ago
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    Integration by parts?

  7. Xavier
    • 3 years ago
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    It can't be expressed in terms of other functions. That integral is the basis of the logarithmic integral function \[li(x)=\int_{0}^{x}\frac{dt}{ln(t)}\]

  8. Kanwar245
    • 3 years ago
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    u = 1/ln x, dv = 1

  9. inkyvoyd
    • 3 years ago
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    No, I'm correct.

  10. inkyvoyd
    • 3 years ago
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    u=lnx du=dx/u Int 1/u dx=int du

  11. geerky42
    • 3 years ago
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    Please explain more clear @inkyvoyd How to use u-substitution?

  12. inkyvoyd
    • 3 years ago
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    int du=u

  13. inkyvoyd
    • 3 years ago
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    gimme a minute lemme use latex

  14. geerky42
    • 3 years ago
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    well then i get u = u it dont do anything.

  15. geerky42
    • 3 years ago
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    I think @Xavier is correct, it can't be expressed

  16. inkyvoyd
    • 3 years ago
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    yes, xavier is in fact correct (facepalm)

  17. inkyvoyd
    • 3 years ago
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    http://www.wolframalpha.com/input/?i=integrate+1%2Fln+x

  18. geerky42
    • 3 years ago
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    Thank you, here's gif

  19. inkyvoyd
    • 3 years ago
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    LOL

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