Question

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

Answer 1

@nbouscal will know what I am talking about, or maybe @Limitless

Answer 2

Wait, correction.

Answer 3

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

Answer 4

Am I supposed to complete the square?

Answer 5

@dpaInc , pwease help me!

Answer 6

can't see it so i'm gonna copy it... and make it huge...
\[\huge \frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1} \]

Answer 7

@dpaInc , how do you copy it like that?

Answer 8

right click-->show math as-->tex commands

Answer 9

\[\huge \int\frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}dv \]

Answer 10

Alright, now solve NAO!

Answer 11

xD

Answer 12

btw, this is the equation I got after trying 3 substitutions and seperating the fraction.

Answer 13

\[\large \int\frac{-\frac{1}{\sqrt{2}}v}{v^2+\sqrt{2}v+1}+\frac{\frac{1}{\sqrt{2}}v}{v^2-\sqrt{2}v+1}dv\]
\[\large \frac{-1}{\sqrt2}\int\frac{v}{v^2+\sqrt{2}v+1}dv+\frac{1}{\sqrt2}\int \frac{v}{v^2-\sqrt{2}v+1}dv\]

maybe i should just draw...

Answer 14

lolol

Answer 15

@dpaInc , now do I complete the square?

Answer 16

yeah... that's what i was about to do...
but i think there is a formula... hang on....

Answer 17

there it is.... #13....:)
http://integral-table.com/downloads/single-page-integral-table.pdf

Answer 18

i mean #16...l

Answer 19

\(\huge \frac{-1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v-\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv\)

Answer 20

But isn't using tables cheating?

Answer 21

no... of course not...

Answer 22

But... I don't know where the tables come from... >.<

Answer 23

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?

Answer 24

No lol. I'M GOING TO BUILD MY CAR FROM SCRATCH MUAHAHAHA

Answer 25

i don't think it's cheating... it's a good shortcut to cut through all that stuff..

Answer 26

Okay... @dpaInc , without showing me the math, can you tell me what to do after I have completed the square?

Answer 27

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...

Answer 28

@dpaInc , my problem is that I'm not sure how to get the results shown in the tables.

Answer 29

let me complete the square on the first integral... i haven't done it for a while and i guess i need the practice...

Answer 30

I already did in my last tex post :)

Answer 31

\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

Answer 32

oh... i see you did it already....

Answer 33

xD

Answer 34

you are solving the problem in a wrong way

Answer 35

@nitz , what am I doing wrong?

Answer 36

see firstly make numerator as the derivative of denominator

Answer 37

Can you show me?

Answer 38

i am talking about 1st integration ie before addition

Answer 39

?

Answer 40

in it, firstly multiply the numerator with 2 and add and subtract \[\sqrt{ 2} \] in it

Answer 41

You mean at the very start of the problem?

Answer 42

ya

Answer 43

but but but

Answer 44

\(\huge \frac{-1}{\sqrt2}\int\frac{v}{(v+\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv+\frac{1}{\sqrt2}\int \frac{v}{(v-\frac{\sqrt{2}}{2})^2+\frac{1}{2}}dv\)
we already got to here >.<

Answer 45

you cant solve it further in this case

Answer 46

#16?
http://integral-table.com/downloads/single-page-integral-table.pdf

Answer 47

these are direct problems

Answer 48

these are direct solutions

Answer 49

you can apply direct formula

Answer 50

i think it works....