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Integrate
\(\frac{\frac{1}{\sqrt{2}v}}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2\sqrt{2}v+1}\)
 one year ago
 one year ago
Integrate \(\frac{\frac{1}{\sqrt{2}v}}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2\sqrt{2}v+1}\)
 one year ago
 one year ago

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inkyvoydBest ResponseYou've already chosen the best response.0
@nbouscal will know what I am talking about, or maybe @Limitless
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
\(\frac{\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2\sqrt{2}v+1}\)
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
Am I supposed to complete the square?
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
@dpaInc , pwease help me!
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
can't see it so i'm gonna copy it... and make it huge... \[\huge \frac{\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2\sqrt{2}v+1} \]
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
@dpaInc , how do you copy it like that?
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
right click>show math as>tex commands
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
\[\huge \int\frac{\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2\sqrt{2}v+1}dv \]
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
Alright, now solve NAO!
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
btw, this is the equation I got after trying 3 substitutions and seperating the fraction.
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
\[\large \int\frac{\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2\sqrt{2}v+1}dv\] \[\large \frac{1}{\sqrt2}\int\frac{v}{v^2+\sqrt{2}v+1}dv+\frac{1}{\sqrt2}\int \frac{v}{v^2\sqrt{2}v+1}dv\] maybe i should just draw...
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
@dpaInc , now do I complete the square?
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
yeah... that's what i was about to do... but i think there is a formula... hang on....
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
there it is.... #13....:) http://integraltable.com/downloads/singlepageintegraltable.pdf
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
\(\huge \frac{1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv\)
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
But isn't using tables cheating?
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
But... I don't know where the tables come from... >.<
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
it's like using all the different tires for your car... you're not going to make/invent your own tires are you? oh wait.. do you drive yet?
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
No lol. I'M GOING TO BUILD MY CAR FROM SCRATCH MUAHAHAHA
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
i don't think it's cheating... it's a good shortcut to cut through all that stuff..
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
Okay... @dpaInc , without showing me the math, can you tell me what to do after I have completed the square?
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
and as for me, i haven't really started using the integral tables until i saw everyon virtually used them here on OS.... i actually went through proving stuff because I don't use/memorize the tables...
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
@dpaInc , my problem is that I'm not sure how to get the results shown in the tables.
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
let me complete the square on the first integral... i haven't done it for a while and i guess i need the practice...
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
I already did in my last tex post :)
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
\huge \frac{1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
oh... i see you did it already....
 one year ago

nitzBest ResponseYou've already chosen the best response.0
you are solving the problem in a wrong way
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
@nitz , what am I doing wrong?
 one year ago

nitzBest ResponseYou've already chosen the best response.0
see firstly make numerator as the derivative of denominator
 one year ago

nitzBest ResponseYou've already chosen the best response.0
i am talking about 1st integration ie before addition
 one year ago

nitzBest ResponseYou've already chosen the best response.0
in it, firstly multiply the numerator with 2 and add and subtract \[\sqrt{ 2} \] in it
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
You mean at the very start of the problem?
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
\(\huge \frac{1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv\) we already got to here >.<
 one year ago

nitzBest ResponseYou've already chosen the best response.0
you cant solve it further in this case
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
#16? http://integraltable.com/downloads/singlepageintegraltable.pdf
 one year ago

nitzBest ResponseYou've already chosen the best response.0
these are direct problems
 one year ago

nitzBest ResponseYou've already chosen the best response.0
these are direct solutions
 one year ago

nitzBest ResponseYou've already chosen the best response.0
you can apply direct formula
 one year ago

dpaIncBest ResponseYou've already chosen the best response.1
i think it works.... dw:1340004704215:dw
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
Uh, I can't use u in substiution LOL. I already used it...
 one year ago

nbouscalBest ResponseYou've already chosen the best response.1
Okay, I'm late to this party, but you can just complete the square and then do a substitution. This is just like the case that we reach in the integration of sqrt(tan x) that we have already done, inky.
 one year ago

LimitlessBest ResponseYou've already chosen the best response.0
Next OS question: What made this integral appealing? I will medal the person with the best response.
 one year ago

nbouscalBest ResponseYou've already chosen the best response.1
This actually looks very similar to the integral of sqrt(tan x), if I had to guess I would say it is an intermediate step in a similar integration.
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
@nbouscal , that was my integration of the square root of tan x...
 one year ago

LimitlessBest ResponseYou've already chosen the best response.0
nbouscal: Integral Detective
 one year ago

inkyvoydBest ResponseYou've already chosen the best response.0
Maybe I should show what work i did before...
 one year ago

nbouscalBest ResponseYou've already chosen the best response.1
I didn't actually go back and look at that integral, you're probably right on. The next step is indeed to complete the square, then do another substitution.
 one year ago

nbouscalBest ResponseYou've already chosen the best response.1
Oh hey just look here: http://openstudy.com/study#/updates/4fb3c611e4b0556534298c6b
 one year ago
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