"how" to integrate:
1/(sinx + cosx)^4

Question

"how" to integrate:
1/(sinx + cosx)^4

anonymous · Answer

accidentally closed this question :/

anonymous · Answer

@amistre64 you know?

amistre64 · Answer

it does seem to be a bit peculiar; im wondering how a u sub would look

amistre64 · Answer

u = sinx + cosx

du = cosx - sinx dx

that doesnt looks to useful to me

amistre64 · Answer

http://www.wolframalpha.com/input/?i=integrate+1%2F%28sinx%2Bcosx%29 that looks nightmarish

amistre64 · Answer

forgot the ^4

amistre64 · Answer

thats better

anonymous · Answer

tried that to a certain extend already, leads me no where (at least for me anyways...)
also, wolframalpha has provided a u sub, where u=tan(y/2) or something like that, but the solution is extremely non-practical....and ofc I'm assuming a better method exist...

amistre64 · Answer

well, i can think of power series, and euler forms

anonymous · Answer

i can do ^1 and ^2, but ^4 is a real pain

amistre64 · Answer

http://www.wolframalpha.com/input/?i=integrate+1%2F%28sinx%2Bcosx%29%5E4 take the derivative of that to see if you can see a clue as to how to reverse it for integration

anonymous · Answer

just when you are happily doing a double integral, you come to a single variable integral you can't do....smh

amistre64 · Answer

can we convert it to a double?  or a polar?

anonymous · Answer

already tried wolframaphla :(, non-practical solution

amistre64 · Answer

can we say:

u = sinx
v = cosx

and do a multivarable integartion?

tkhunny · Answer

You can ALWAYS use the the tan(y/2), but seriously?  Why not simplify your life?

$\sin(x) + \cos(x) = \sqrt{2}\cdot\cos(x - \pi/4) $

amistre64 · Answer

... not that i can type it :/

amistre64 · Answer

that was one form i never learnt :)

anonymous · Answer

lol, never seem that form as well, gona try it now....