Here's the question you clicked on:
experimentX
find the shortest method to evaluate this \[ \int \frac{\sin x}{\sin x + \cos x} \; dx\]
|dw:1347566427407:dw|
Do you know anything shorter?
nope ... haven't found any other.
just noted how similar these two integrals look like \[ \int \frac{\sin x}{\sin x + \cos x} \; dx \\ \int \frac{\cos x}{\sin x + \cos x} \; dx \]
Note one more way. Although the same really, |dw:1347566670806:dw|
^^ No limits here.
well ... pretty clever manipulation on the last problem
lol i thought there are ;)
yeah ... that is also very nice problem. i wish this one had too http://math.stackexchange.com/questions/198083/integrate-sin3x-sin3x-cos3x/198122#198122
interesting technique ...
maybe it does. |dw:1347567374847:dw|
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
For 2, Taking six + cosx as t, |dw:1347567485586:dw|
this is just a back hack
find the answer first ... differentiate the answer to get the get the middle portion.
How do you find the answer first?
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.
Okay. Back hack, eh. Hmmmm.
Weierstrass substitution gives solution of any type ... but that is the last resort. very ugly method.
well ... good night!!
Yeah. Goodnight. I'll think about this and get back to you tommorow. :)
Hold onn. What about the current solution to that, It does work quite easily or not?
To the sin^3x/sin^3x + cos^3x
there isn't nice manipulation like sin(x)/sin(x)+cos(x) for this one.