anonymous
  • anonymous
more calculus help
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
\[\int\limits_{?}^{?}(1)/(xln(x ^{4}))\]
bahrom7893
  • bahrom7893
that 1/x is buggin me as a u sub.. but it's prolly integration by parts
anonymous
  • anonymous
start with \[\frac{1}{x\ln(x^4)}=\frac{1}{4x\ln(x)}\] then it should be easy

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bahrom7893
  • bahrom7893
Let u = ln(x^4)
bahrom7893
  • bahrom7893
Ha I think i got this one!
bahrom7893
  • bahrom7893
u = ln(x^4) du = 4/x simple u sub!
anonymous
  • anonymous
good. because i am clueless???
anonymous
  • anonymous
pull the 1/4 outside of the integral get \[\frac{1}{4}\int \frac{dx}{x\ln(x)}\] then make \[u=\ln(x),du=\frac{1}{x}dx\] and you are home free
bahrom7893
  • bahrom7893
well yea pretty much the same thing as satellite did
anonymous
  • anonymous
don't forget the properties of the log!
bahrom7893
  • bahrom7893
lol my method works too though :)
anonymous
  • anonymous
oookkk i got it
anonymous
  • anonymous
yes it will work and you will see that if \[u=\ln(x^4)\] then \[du=\frac{4}{x}dx\] but that is telling you that \[\ln(x^4)=4\ln(x)\]
anonymous
  • anonymous
would the fianl answer be 1/4ln (ln(x))+c?
anonymous
  • anonymous
Final*
anonymous
  • anonymous
it would be, yes
anonymous
  • anonymous
sweet thanks again.
anonymous
  • anonymous
btw if you notice you will get a different answer from wolfram and if you like i can explain why
anonymous
  • anonymous
please do
anonymous
  • anonymous
here is what wolfram writes if you just type it in. you get \[\frac{1}{4}\ln(\ln(x^4))+c\]
anonymous
  • anonymous
but \[\ln(\ln(x^4))=\ln(4\ln(x))=\ln(4)+\ln(\ln(x))\] and \[\ln(4) \] is a constant. so answers are the same, since the constant is just a constant, like the +C out at the end
anonymous
  • anonymous
oo ok that is simple enough thanks again

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