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experimentX
Group Title
find the shortest method to evaluate this
\[ \int \frac{\sin x}{\sin x + \cos x} \; dx\]
 one year ago
 one year ago
experimentX Group Title
find the shortest method to evaluate this \[ \int \frac{\sin x}{\sin x + \cos x} \; dx\]
 one year ago
 one year ago

This Question is Closed

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
dw:1347566427407:dw
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
yeah that it is.
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
Do you know anything shorter?
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
nope ... haven't found any other.
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
just noted how similar these two integrals look like \[ \int \frac{\sin x}{\sin x + \cos x} \; dx \\ \int \frac{\cos x}{\sin x + \cos x} \; dx \]
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
Note one more way. Although the same really, dw:1347566670806:dw
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
2I=pi/2 :)
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
^^ No limits here.
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
well ... pretty clever manipulation on the last problem
 one year ago

mukushla Group TitleBest ResponseYou've already chosen the best response.0
lol i thought there are ;)
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
yeah ... that is also very nice problem. i wish this one had too http://math.stackexchange.com/questions/198083/integratesin3xsin3xcos3x/198122#198122
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
interesting technique ...
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
maybe it does. dw:1347567374847:dw
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
there is one http://www.wolframalpha.com/input/?i=integrate%20%201/3%2bsin%28x%29/%283%28sin%28x%29%20%2b%20cos%28x%29%29%29%20%202cos%282x%29/%283%2a%282%20%20sin%282x%29%29%29 not nice and intuitive though
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
For 2, Taking six + cosx as t, dw:1347567485586:dw
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
this is just a back hack
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
back hack?
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
find the answer first ... differentiate the answer to get the get the middle portion.
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
How do you find the answer first?
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
make it easy as much a possible ... that's how i approach most of the problems. i to honest ... i can't work without answer.
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
Okay. Back hack, eh. Hmmmm.
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
Weierstrass substitution gives solution of any type ... but that is the last resort. very ugly method.
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
Agreed.
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
well ... good night!!
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
Yeah. Goodnight. I'll think about this and get back to you tommorow. :)
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
Hold onn. What about the current solution to that, It does work quite easily or not?
 one year ago

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
To the sin^3x/sin^3x + cos^3x
 one year ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
there isn't nice manipulation like sin(x)/sin(x)+cos(x) for this one.
 one year ago
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