anonymous
  • anonymous
Find the following integral
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
what is the integer?
anonymous
  • anonymous
\[\int\limits_{}^{} \frac{ (2t+1)^{2} }{ \sqrt{t} } dt\]
anonymous
  • anonymous
does \[\frac{ t ^{2} }{ \sqrt{t} } \] cancel out????

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RadEn
  • RadEn
u need to expand of (2t + 1)^2 = 4t^2 + 4t + 1 and convert sqrt(t) = t^(1/2) now, can u simplify (4t^2 + 4t + 1)/t^(1/2) ?
anonymous
  • anonymous
yea i think it does lol
anonymous
  • anonymous
well I'll show you how far I got \[4 \int\limits_{}^{} \frac{ t ^{2} }{ t ^{1/2} } +4 \int\limits_{}^{} \frac{ t }{ t ^{1/2} } + \int\limits_{}^{} \frac{ 1 }{ t ^{1/2} }\]
RadEn
  • RadEn
so far is good, then use the properties of exponent to simplify of them : |dw:1358987039172:dw|
RadEn
  • RadEn
now, what would be ur integral ?
anonymous
  • anonymous
Sorry openstudy crapped out last night lol thanks
RadEn
  • RadEn
nopes.. :) btw, do u got it ?
anonymous
  • anonymous
Mhmm :) I got \[\frac{ 8t ^{^{5/2}} }{ 5 }+\frac{ 8t ^{3/2} }{ 3 }+ 2t ^{1/2}+c\] Look about right?
RadEn
  • RadEn
yeah, i have cheked ur answer you are right :)
anonymous
  • anonymous
Hehe you are the best thanks!!!!
RadEn
  • RadEn
you're welcome

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