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

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inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0@nbouscal will know what I am talking about, or maybe @Limitless

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0\(\frac{\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2\sqrt{2}v+1}\)

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Am I supposed to complete the square?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0@dpaInc , pwease help me!

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

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0@dpaInc , how do you copy it like that?

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1right click>show math as>tex commands

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

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Alright, now solve NAO!

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0btw, this is the equation I got after trying 3 substitutions and seperating the fraction.

dpaInc
 2 years ago
Best 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...

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0@dpaInc , now do I complete the square?

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

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1there it is.... #13....:) http://integraltable.com/downloads/singlepageintegraltable.pdf

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

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0But isn't using tables cheating?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0But... I don't know where the tables come from... >.<

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1it'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?

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0No lol. I'M GOING TO BUILD MY CAR FROM SCRATCH MUAHAHAHA

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1i don't think it's cheating... it's a good shortcut to cut through all that stuff..

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

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1and 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...

inkyvoyd
 2 years ago
Best 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.

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

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0I already did in my last tex post :)

inkyvoyd
 2 years ago
Best 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

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1oh... i see you did it already....

nitz
 2 years ago
Best ResponseYou've already chosen the best response.0you are solving the problem in a wrong way

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0@nitz , what am I doing wrong?

nitz
 2 years ago
Best ResponseYou've already chosen the best response.0see firstly make numerator as the derivative of denominator

nitz
 2 years ago
Best ResponseYou've already chosen the best response.0i am talking about 1st integration ie before addition

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

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0You mean at the very start of the problem?

inkyvoyd
 2 years ago
Best 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 >.<

nitz
 2 years ago
Best ResponseYou've already chosen the best response.0you cant solve it further in this case

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0#16? http://integraltable.com/downloads/singlepageintegraltable.pdf

nitz
 2 years ago
Best ResponseYou've already chosen the best response.0these are direct solutions

nitz
 2 years ago
Best ResponseYou've already chosen the best response.0you can apply direct formula

dpaInc
 2 years ago
Best ResponseYou've already chosen the best response.1i think it works.... dw:1340004704215:dw

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Uh, I can't use u in substiution LOL. I already used it...

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1Okay, 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.

Limitless
 2 years ago
Best ResponseYou've already chosen the best response.0Next OS question: What made this integral appealing? I will medal the person with the best response.

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1This 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.

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0@nbouscal , that was my integration of the square root of tan x...

Limitless
 2 years ago
Best ResponseYou've already chosen the best response.0nbouscal: Integral Detective

inkyvoyd
 2 years ago
Best ResponseYou've already chosen the best response.0Maybe I should show what work i did before...

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1I 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.

nbouscal
 2 years ago
Best ResponseYou've already chosen the best response.1Oh hey just look here: http://openstudy.com/study#/updates/4fb3c611e4b0556534298c6b
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