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wioBest ResponseYou've already chosen the best response.0
Find the roots, then you can factor it. Then you want to try partial fraction decomposition.
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
I am lost at completing the square.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large x^2+bx\]To complete the square, we take half of the \(\large b\) term, and square it. \[\large x^2+bx+\left(\frac{b}{2}\right)^2\]Now we can't just add this number, it will change the value of our polynomial, we want to keep it balanced. So we have to also subtract this number. \[\large \color{royalblue}{x^2+bx+\left(\frac{b}{2}\right)^2}\left(\frac{b}{2}\right)^2\]The reason for doing this is, the blue part will now factor down into a perfect square. A binomial containing x and half of the b term.\[\large \color{royalblue}{\left(x+\frac{b}{2}\right)^2}\left(\frac{b}{2}\right)^2\]
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
Let's see if we can apply this to our problem here.
 one year ago

zepdrixBest ResponseYou've already chosen the best response.1
\[\large x^2+x+1\]The \(\large b\) coefficient appears to be 1. (The middle term ~ because \(\large x\) is the same as \(\large 1\cdot x\) ). So to to complete the square, we'll take half of 1, and square it.\[\large \color{orangered}{x^2+x+\left(\frac{1}{2}\right)^2}\left(\frac{1}{2}\right)^2+1\]I moved the 1 out of the way, we don't want to deal with that right now. Ok the orange part should give us a perfect square now,\[\large \color{orangered}{\left(x+\frac{1}{2}\right)^2}\left(\frac{1}{2}\right)^2+1\] Which will simplify further to,\[\large \left(x+\frac{1}{2}\right)^2+\frac{3}{4}\]
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
\[4/3 \int\limits_{}^{}1/((4/3) u^2 +1) du\] What next?
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
(3/4)∫1/((4/3)u2+1)du I think this is right. What do I do next?
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
this seems much more easier than what is being done... but thats just me
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
\[\frac{4}{3}\int\frac{1}{\frac{4}{3}u^2+1}du=\frac{\frac{4}{3}}{\frac{4}{3}} \int \frac{1}{u^2+1}du\]
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
I agree. the book (answer in the back) and wolfram alpha I believe use a substitution here of 2/sqrt3 which gets complicated..
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
is it \[\frac{1}{4/3(u^2+1)}\]
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
1/x2+x+1 tp begin with.
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
Does that answer your question?
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
what is problem... like that is in the book
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
without anything done to it
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
\[\int\limits_{}^{} (x^2 x + 2) / (x^3 1) \ \ dx\]
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
I understand the partial fraction decomposition element to this. I am still lost at the point mentioned to complete the square. I haven't been taught yet.
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
alright well whered the partials you used?
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
I ask this because if you use partials you should've gotten a natural log for one of the fractions
 one year ago

wioBest ResponseYou've already chosen the best response.0
When you have \(u^2+1\) it's a sign to try the trig sub \(u=\tan\theta\).
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
yeah the answer so far is .. \[2/3 \ln (x+1) + 1/6 \ln (x^2 + x + 1) 9/2\int\limits_{}^{} dx / (x^2 + x + 1) \]
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
sorry 2/sqrt3 = u for the substitution?
 one year ago

wioBest ResponseYou've already chosen the best response.0
What is the original integral?
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
∫(x2−x+2)/(x3−1) dx
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
the last part you have to
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
complete the square and use trig sub
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
\[x^2+x+1\] half of b = 1/2.. \[\frac{b}{4}^2=(\frac{b}{2})^2=\frac{1}{4}\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
if you add that you must subtract \[\frac{1}{x^2+x+\frac{1}{4}+1\frac{1}{4}}\]
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
this is where he ot \[\frac{1}{(x+\frac{1}{2})^2+\frac{3}{4}}\]
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
then factor out the 3/4 in the bottom.
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
ok now you get to where you were before right?
 one year ago

Outkast3r09Best ResponseYou've already chosen the best response.0
now let \[x=\frac{a}{b}tan(\theta)\]
 one year ago

LACHEEK989Best ResponseYou've already chosen the best response.0
is a/b 3/4 or does should I do a substitution like 2/sqrt 3 ?
 one year ago
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