anonymous
  • anonymous
evaluate indefinite integrals integral squareroot x^4/ x^3-1 dx
Calculus1
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
what is it ?
anonymous
  • anonymous
thanks
RadEn
  • RadEn
is the x^3-1 in the sqrt also or no ??

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anonymous
  • anonymous
yes, it is.
RadEn
  • RadEn
|dw:1355676028137:dw|
anonymous
  • anonymous
okay,
RadEn
  • RadEn
now, use int by subs let u=x^3-1 du = 3x^2 dx or x^2 dx = 1/3 du continue it.....
anonymous
  • anonymous
-1/3 intergral 1/ sqrt of u * du
RadEn
  • RadEn
miss (-) sign, how come this ?
anonymous
  • anonymous
i took du as -3x^2
RadEn
  • RadEn
derivative of x^3 is 3x^2, right ?
anonymous
  • anonymous
yes
RadEn
  • RadEn
so, why becomes (-) ?
anonymous
  • anonymous
well, i wrote the problem as 1-x^3 instead of x^3 -1
RadEn
  • RadEn
lol, hahaha...
anonymous
  • anonymous
hmm
RadEn
  • RadEn
so, the original problem is over x^3-1 or 1-x^3 ?
anonymous
  • anonymous
it is x^3 -1
RadEn
  • RadEn
ok, therefore the integration can be |dw:1355676826761:dw|
RadEn
  • RadEn
i just gave u +c :), for the rest let try it
anonymous
  • anonymous
u= x^3 -1 here
RadEn
  • RadEn
yes
RadEn
  • RadEn
because i have saw ur problem is .... over x^3-1, but experiment gave u 1-x^3
anonymous
  • anonymous
i know
anonymous
  • anonymous
and i put it in the wolfram thing, got some different ans
RadEn
  • RadEn
what's the result of int above, dont use wolfram first
anonymous
  • anonymous
(u) ^-1/2 +1/ -1/2+1
RadEn
  • RadEn
where is the 1/3 ?
anonymous
  • anonymous
(x^3-1)+c
anonymous
  • anonymous
What do I do with that 1/3?
anonymous
  • anonymous
can you please write down the whole problem and show how it works, if you do not mind then
anonymous
  • anonymous
i am kind of confused
RadEn
  • RadEn
|dw:1355677696473:dw|
RadEn
  • RadEn
got it ?
anonymous
  • anonymous
how did u get that 2u?
RadEn
  • RadEn
1/(-1/2 + 1) = 1/(1/2) = 1 * 2/1 = 2 right ?
anonymous
  • anonymous
yeah, sorry
anonymous
  • anonymous
i have another problem, will you guide me through that one? i will try solving it and show it to you.
RadEn
  • RadEn
nopes... now, subtitute back that u=x^3-1 so, the answer be 2/3 (x^3-1)^(1/2) + c or 2/3*sqrt(x^3-1) + c
RadEn
  • RadEn
wolfram is same with the answer above :)
anonymous
  • anonymous
k.
anonymous
  • anonymous
okay
anonymous
  • anonymous
thank you.
RadEn
  • RadEn
very welcome

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