anonymous
  • anonymous
what is the integral of 1/x^2
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
i dont even think its possible -.-
anonymous
  • anonymous
-1/x+C
anonymous
  • anonymous
that makes sense...

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anonymous
  • anonymous
lol, you can let u = x and du = dx and solve :) loki will show you the steps ^_^
anonymous
  • anonymous
You just look at it like this,\[\int\limits_{}{}\frac{1}{x^2}dx=\int\limits_{}{}x^{-2}dx=\frac{x^{-1}}{-1}+c=-x^{-1}+c=-\frac{1}{x}+c\]
anonymous
  • anonymous
integral x^(-2) Just add one to the exponent and divide by the result
anonymous
  • anonymous
Yep.
anonymous
  • anonymous
what method is that?
anonymous
  • anonymous
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.
anonymous
  • anonymous
?????????
anonymous
  • anonymous
Usual method...just the same you're used to when you integrate something like\[\int\limits_{}{}x dx\]
anonymous
  • anonymous
\[\int\limits_{}{}x^ndx=\frac{1}{n+1}x^{n+1}+c\]where n is any (real) number.
anonymous
  • anonymous
Here you started with n=-2.
anonymous
  • anonymous
Damn I overcomplicated that
anonymous
  • anonymous
Hehe...slightly ;)
anonymous
  • anonymous
slightly... dudee i used u sub, uv vdu sub, pfd, random stuff i could come up with.. i WAYYYY overcomplicated it :P
anonymous
  • anonymous
lol, you should calm down.
anonymous
  • anonymous
probably, so the integral of lnx/x^2 is lnx/x - 1/x +c
anonymous
  • anonymous
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.
anonymous
  • anonymous
I get a minus outside of your lnx/x
anonymous
  • anonymous
you say that to everyone who askes for conformation lol and my bad, i left it back in uv vdu sub -.-
anonymous
  • anonymous
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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