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anonymous

  • 5 years ago

what is the integral of 1/x^2

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  1. anonymous
    • 5 years ago
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    i dont even think its possible -.-

  2. anonymous
    • 5 years ago
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    -1/x+C

  3. anonymous
    • 5 years ago
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    that makes sense...

  4. anonymous
    • 5 years ago
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    lol, you can let u = x and du = dx and solve :) loki will show you the steps ^_^

  5. anonymous
    • 5 years ago
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    You just look at it like this,\[\int\limits_{}{}\frac{1}{x^2}dx=\int\limits_{}{}x^{-2}dx=\frac{x^{-1}}{-1}+c=-x^{-1}+c=-\frac{1}{x}+c\]

  6. anonymous
    • 5 years ago
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    integral x^(-2) Just add one to the exponent and divide by the result

  7. anonymous
    • 5 years ago
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    Yep.

  8. anonymous
    • 5 years ago
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    what method is that?

  9. anonymous
    • 5 years ago
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    Same deal. Don't be put off by the negative sign. Also, if you ever have a number that's not an integer, don't be put off by that either: add 1 and divide by the result.

  10. anonymous
    • 5 years ago
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    ?????????

  11. anonymous
    • 5 years ago
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    Usual method...just the same you're used to when you integrate something like\[\int\limits_{}{}x dx\]

  12. anonymous
    • 5 years ago
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    \[\int\limits_{}{}x^ndx=\frac{1}{n+1}x^{n+1}+c\]where n is any (real) number.

  13. anonymous
    • 5 years ago
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    Here you started with n=-2.

  14. anonymous
    • 5 years ago
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    Damn I overcomplicated that

  15. anonymous
    • 5 years ago
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    Hehe...slightly ;)

  16. anonymous
    • 5 years ago
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    slightly... dudee i used u sub, uv vdu sub, pfd, random stuff i could come up with.. i WAYYYY overcomplicated it :P

  17. anonymous
    • 5 years ago
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    lol, you should calm down.

  18. anonymous
    • 5 years ago
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    probably, so the integral of lnx/x^2 is lnx/x - 1/x +c

  19. anonymous
    • 5 years ago
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    You can check by taking the derivative of your answer. If it's right, it should equal the integrand (the expression inside the integral). It's the Fundamental Theorem of the Calculus.

  20. anonymous
    • 5 years ago
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    I get a minus outside of your lnx/x

  21. anonymous
    • 5 years ago
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    you say that to everyone who askes for conformation lol and my bad, i left it back in uv vdu sub -.-

  22. anonymous
    • 5 years ago
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    You should learn a method called, 'Tabular Integration by Parts'. If you understand the theory, it's good to know this method because you can punch out IBP problems with a lot less hassle. There's a good explanation about it here: http://en.wikipedia.org/wiki/Integration_by_parts under, ironically, 'Tabular Integration by Parts'.

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