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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

siddhantsharan Group TitleBest ResponseYou've already chosen the best response.3
Agreed.
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.0
well ... good night!!
 2 years 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. :)
 2 years 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?
 2 years ago

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