A goodnight integral problem. Enjoy.

>>9085641
>cot

kys

divergent improper integral.

post something interesting next time, piggot

3?

>>9085711
FUCK I made a mistake :(

>>9085711
>>9085723
OK now I say it's pi/4

piggot

>>9085672
Cot is cancer

http://www.wolframalpha.com/input/?i=integrate+sqrt(cot(x))+%2F+(sqrt(cot(x))%2Bsqrt(tan(x)))+from+0+to+pi%2F2

pi/4

>cot
Do Americans really write this?

>>9085874
I think it's an Engineering thing. I've never encountered it in higher math textbooks (it's just written out as 1/tan), but it's taught in Calculus, being a cross-disciplinary requirement.

>>9085641
[math]\frac{\pi}{4}[/math]

Map x to pi/2 - x
Add to original integral

>>9085672
Welcome to America, the land of the scientists

>>9085641
tan(x) = u^2
sec^2(x)dx = 2*udu
dx = 2*u/(1 + u^4) du = 2*u/[(u^2 - sqrt(2)*u + 1)*(u^2 + sqrt(2)*u +1)]
so the integral becomes integral 0 to infinity 2*u/[(1+u^2)*(u^2 - sqrt(2) + 1)*(u^2 + sqrt(2)*u + 1)] du.
Then, you just do partial fractions here.

I think I saw this in that Inside Interesting Integrals book. Don't you reverse the direction of integration?

>>9085641
Multiply top and bottom by rad(cotx) and then it becomes brainlet tier

>he doesn't write cot
what the fuck do you write? cos/sin? fucking brainlets

>>9086909
cotg

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im 26 and i just finished high school so bear with me but doesnt the whole thing simplify to 1?

>>9087062
no
you seem to be doing algebra without a clear understanding of the link between the steps, and instead just guesing what the next line should show

>>9087067
i dont understand. what part did i get wrong?

>>9087069
mathematics isn't a guessing game mate, if you can't tell exactly how you got from one line to another it's going to be wrong.

>>9087069
Since he's being an asshole, the issue is going form the right on the second line after you wrote simplifying to the left on the third line. You missed the +1 with the tanx.

>>9087077
oh i see. thanks

>>9087077
he also has a mistake on the third line when he uses the resiprocal of one of the fractions

why bother fixing the mistakes of someone who is still not at a level where he can follow the principles of mathematical logic? correcting a couple of errors isn't going to make him a better mathematician when he doesn't understand what "therefore" means

>>9087083
theres only one thing more retarded i guess, and that would be posting about it

>>9087086
posting about retards making mistakes makes me retarded? maybe, but at least I can do basic algebra

>>9087083
>resiprocal
reciprocal

>>9087090
гoвopить co мнoй, кoгдa ты мoжeшь гoвopить нa pyccкoм, дypaк блять

>>9087089
You're just being a hostile asshole for no reason. People makes mistakes then they learn from them. You're no different you passive aggressive faggot.

>>9087104
calm down perelman

>>9087104
What the fuck did you just fucking say about me, you little bitch? I’ll have you know I graduated top of my class in the Navy Seals, and I’ve been involved in numerous secret raids on Al-Quaeda, and I have over 300 confirmed kills. I am trained in gorilla warfare and I’m the top sniper in the entire US armed forces. You are nothing to me but just another target. I will wipe you the fuck out with precision the likes of which has never been seen before on this Earth, mark my fucking words. You think you can get away with saying that shit to me over the Internet? Think again, fucker. As we speak I am contacting my secret network of spies across the USA and your IP is being traced right now so you better prepare for the storm, maggot. The storm that wipes out the pathetic little thing you call your life. You’re fucking dead, kid. I can be anywhere, anytime, and I can kill you in over seven hundred ways, and that’s just with my bare hands. Not only am I extensively trained in unarmed combat, but I have access to the entire arsenal of the United States Marine Corps and I will use it to its full extent to wipe your miserable ass off the face of the continent, you little shit. If only you could have known what unholy retribution your little “clever” comment was about to bring down upon you, maybe you would have held your fucking tongue. But you couldn’t, you didn’t, and now you’re paying the price, you goddamn idiot. I will shit fury all over you and you will drown in it. You’re fucking dead, kiddo.

>>9087104
I love baiting you asspies lel

Let [math]A \,\in\, \left[0,\, \frac\pi2 \right[[/math]. With [math]t \,=\, \sqrt{\tan\,x}[/math] and a PFD,
[eqn]\int_0^A \frac{\sqrt{\cot\,x}} {\sqrt{\cot\,x} \,+\, \sqrt{\tan\,x}} \,\mathrm dx \,=\, \frac12\, \int_0^\sqrt{\tan\,A} \frac t{t^2 \,+\, 1} \,\mathrm dt \,-\, \frac1{4\,\sqrt2}\, \int_0^\sqrt{\tan\,A} \frac{\sqrt2\,t \,-\, 2}{t^2 \,-\, \sqrt2\,t \,+\, 1} \,\mathrm dt \,-\, \frac1{4\,\sqrt2}\, \int_0^\sqrt{\tan\,A} \frac{\sqrt2\,t \,-\, 2}{t^2 \,+\, \sqrt2\,t \,+\, 1} \,\mathrm dt[/eqn]
The first integral gives:
[eqn]\int_0^\sqrt{\tan\,A} \frac t{t^2 \,+\, 1} \,\mathrm dt \,=\, \frac{\ln \left| \tan\,A \,+\, 1 \right|}2[/eqn]
The second integral gives:
[eqn]\int_0^\sqrt{\tan\,A} \frac{\sqrt2\,t \,-\, 2}{t^2 \,-\, \sqrt2\,t \,+\, 1} \,\mathrm dt \,=\, \frac{\sqrt2}2\, \ln\left| \tan\,A\,\left( 1 \,-\, \sqrt{\frac2{\tan\,A}} \,+\, \frac1{\tan\,A} \right) \right| \,-\, \sqrt2\, \arctan\left( \sqrt{2\,\tan\,A} \,-\, 1 \right) \,-\, \frac{\pi\,\sqrt2}4[/eqn]
Similarly, the third integral gives:
[eqn]\int_0^\sqrt{\tan\,A} \frac{\sqrt2\,t \,-\, 2}{t^2 \,+\, \sqrt2\,t \,+\, 1} \,\mathrm dt \,=\, \frac{\sqrt2}2\, \ln\left| \tan\,A\,\left( 1 \,+\, \sqrt{\frac2{\tan\,A}} \,+\, \frac1{\tan\,A} \right) \right| \,-\, 3\,\sqrt2\, \arctan\left( \sqrt{2\,\tan\,A} \,+\, 1 \right) \,+\, \frac{3\,\pi\,\sqrt2}4[/eqn]
Summing makes the logs converge towards 0, hence
[eqn]\int_0^A \frac{\sqrt{\cot\,x}} {\sqrt{\cot\,x} \,+\, \sqrt{\tan\,x}} \,\mathrm dx \,\underset{A \,\to\, \infty}{\sim}\, \sqrt2\, \arctan\left( \sqrt{2\,\tan\,A} \,-\, 1 \right) \,+\, \frac{\pi\,\sqrt2}4 \,+\, \frac34\, \arctan\left( \sqrt{2\,\tan\,A} \,+\, 1 \right) \,-\, \frac{3\,\pi}{16} \,\xrightarrow[A \,\to\, \infty]{}\, \frac{\pi\,\sqrt2}2 \,+\, \frac{\pi\,\sqrt2}4 \,+\, \frac{3\,\pi}8 \,-\, \frac{3\,\pi}{16}[/eqn]
Therefore,
[eqn]\int_0^{\frac\pi2} \frac{\sqrt{\cot\,x}} {\sqrt{\cot\,x} \,+\, \sqrt{\tan\,x}} \,\mathrm dx \,=\, \frac{12\,\sqrt2 \,+\, 3}{16} \,\pi[/eqn]

>>9087293
"No."

The answer is [math]\frac{\pi}{4}[/math]

>>9087397
Then be useful and find where the mistake is.

>>9086621
see >>9086071

>>9087415
You need to clear the discontinuity. So multiply the original equation by [math]tan(x) sec^2(x)[/math] and try again.

>>9087293
Lmao
autism doesn't mean you're right

>>9087448
* in the numerator and denominator in case that isn't clear.

>>9085711
>>9085732
>piggot autist is bad at math
Who would've thunk

>>9085672
>>9085828
>>9085874
What's wrong with cot?

test

>>9087083
Hows undergrad treating you

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Hey I'm the only one allowed to make these threads.

>>9087827
Trigonometry formulas are complicated enough with 3 functions.

>>9087104
too lazy to download your shit keyboard

Ya ponimayu chto ti pisel, i ya znayu kak govorit po russkiy (no ochen ploho)

You are not smarter than us because you know 2 languages, this is a science board, not linguistics. If you wanna talk in English don't be a dick when some asshole corrects your spelling.

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>>9089815
Literally Integration by Parts
sky

>>9085874
What the FUCK do Europeans write then for the reciprocal of tangent?

>>9087104
>Гoвopить

>>9085874
absolutely.

>>9085641
https://www.wolframalpha.com/input/?i=\int^{\pi/2}_{0}+\frac{sqrt(cot(x))}{sqrt(cot(x))+sqrt(tan(x))}+dx

ayyylmao

>>9090437
>not switching to a trivial complex problem and taking the imaginary part of the result
Back to high school.