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

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0I am lost at completing the square.

zepdrix
 one year ago
Best 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.\[\large \color{royalblue}{\left(x+\frac{b}{2}\right)^2}\left(\frac{b}{2}\right)^2\]

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

zepdrix
 one year ago
Best 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,\[\large \left(x+\frac{1}{2}\right)^2+\frac{3}{4}\]

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0\[4/3 \int\limits_{}^{}1/((4/3) u^2 +1) du\] What next?

LACHEEK989
 one year ago
Best 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?

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0this seems much more easier than what is being done... but thats just me

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{4}{3}\int\frac{1}{\frac{4}{3}u^2+1}du=\frac{\frac{4}{3}}{\frac{4}{3}} \int \frac{1}{u^2+1}du\]

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0I agree. the book (answer in the back) and wolfram alpha I believe use a substitution here of 2/sqrt3 which gets complicated..

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0is it \[\frac{1}{4/3(u^2+1)}\]

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.01/x2+x+1 tp begin with.

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0Does that answer your question?

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0what is problem... like that is in the book

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0without anything done to it

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{}^{} (x^2 x + 2) / (x^3 1) \ \ dx\]

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0I 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.

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0alright well whered the partials you used?

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0I ask this because if you use partials you should've gotten a natural log for one of the fractions

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

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0yeah the answer so far is .. \[2/3 \ln (x+1) + 1/6 \ln (x^2 + x + 1) 9/2\int\limits_{}^{} dx / (x^2 + x + 1) \]

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0sorry 2/sqrt3 = u for the substitution?

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

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0∫(x2−x+2)/(x3−1) dx

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0the last part you have to

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0complete the square and use trig sub

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0\[x^2+x+1\] half of b = 1/2.. \[\frac{b}{4}^2=(\frac{b}{2})^2=\frac{1}{4}\]

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0if you add that you must subtract \[\frac{1}{x^2+x+\frac{1}{4}+1\frac{1}{4}}\]

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0this is where he ot \[\frac{1}{(x+\frac{1}{2})^2+\frac{3}{4}}\]

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0then factor out the 3/4 in the bottom.

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0ok now you get to where you were before right?

Outkast3r09
 one year ago
Best ResponseYou've already chosen the best response.0now let \[x=\frac{a}{b}tan(\theta)\]

LACHEEK989
 one year ago
Best ResponseYou've already chosen the best response.0is a/b 3/4 or does should I do a substitution like 2/sqrt 3 ?
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