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

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

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

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

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

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

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

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

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

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

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

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0there 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

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

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0find the answer first ... differentiate the answer to get the get the middle portion.

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

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

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

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0Weierstrass substitution gives solution of any type ... but that is the last resort. very ugly method.

experimentX
 2 years ago
Best ResponseYou've already chosen the best response.0well ... good night!!

siddhantsharan
 2 years ago
Best ResponseYou've already chosen the best response.3Yeah. Goodnight. I'll think about this and get back to you tommorow. :)

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

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

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