Open study

is now brainly

With Brainly you can:

  • Get homework help from millions of students and moderators
  • Learn how to solve problems with step-by-step explanations
  • Share your knowledge and earn points by helping other students
  • Learn anywhere, anytime with the Brainly app!

A community for students.

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

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Join Brainly to access

this expert answer

SEE EXPERT ANSWER

To see the expert answer you'll need to create a free account at Brainly

@nbouscal will know what I am talking about, or maybe @Limitless
Wait, correction.
\(\frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}\)

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Am I supposed to complete the square?
@dpaInc , pwease help me!
can't see it so i'm gonna copy it... and make it huge... \[\huge \frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1} \]
@dpaInc , how do you copy it like that?
right click-->show math as-->tex commands
\[\huge \int\frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}dv \]
Alright, now solve NAO!
xD
btw, this is the equation I got after trying 3 substitutions and seperating the fraction.
\[\large \int\frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}dv\] \[\large \frac{-1}{\sqrt2}\int\frac{v}{v^2+\sqrt{2}v+1}dv+\frac{1}{\sqrt2}\int \frac{v}{v^2-\sqrt{2}v+1}dv\] maybe i should just draw...
lolol
@dpaInc , now do I complete the square?
yeah... that's what i was about to do... but i think there is a formula... hang on....
there it is.... #13....:) http://integral-table.com/downloads/single-page-integral-table.pdf
i mean #16...l
\(\huge \frac{-1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v-\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv\)
But isn't using tables cheating?
no... of course not...
But... I don't know where the tables come from... >.<
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?
No lol. I'M GOING TO BUILD MY CAR FROM SCRATCH MUAHAHAHA
i don't think it's cheating... it's a good shortcut to cut through all that stuff..
Okay... @dpaInc , without showing me the math, can you tell me what to do after I have completed the square?
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...
@dpaInc , my problem is that I'm not sure how to get the results shown in the tables.
let me complete the square on the first integral... i haven't done it for a while and i guess i need the practice...
I already did in my last tex post :)
\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
oh... i see you did it already....
xD
you are solving the problem in a wrong way
@nitz , what am I doing wrong?
see firstly make numerator as the derivative of denominator
Can you show me?
i am talking about 1st integration ie before addition
?
in it, firstly multiply the numerator with 2 and add and subtract \[\sqrt{ 2} \] in it
You mean at the very start of the problem?
ya
but but but
\(\huge \frac{-1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v-\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv\) we already got to here >.<
you cant solve it further in this case
#16? http://integral-table.com/downloads/single-page-integral-table.pdf
these are direct problems
these are direct solutions
you can apply direct formula
i think it works.... |dw:1340004704215:dw|
Uh, I can't use u in substiution LOL. I already used it...
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.
Next OS question: What made this integral appealing? I will medal the person with the best response.
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.
@nbouscal , that was my integration of the square root of tan x...
nbouscal: Integral Detective
Maybe I should show what work i did before...
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.

Not the answer you are looking for?

Search for more explanations.

Ask your own question