Question

\[\int e^x cos(x) dx\]

Answer 1

Cool way to do it

Answer 2

this must be solved by parts

Answer 3

without int by parts

Answer 4

how then? O.o

Answer 5

uv-\[\int\limits\limits_{}^{}vdu\]

Answer 6

i would let u be x and let dv be cos (x)

Answer 7

yea but Imran said not by parts...

Answer 8

(1/2)e^x(sin(x) + cos(X)) + C
C = Constant

Answer 9

\[e^{i\space x}= cos x + i sin x\]
Real[e^(i x)]= cos x
\[\int e^{ix} e^x dx\]
\[\int e^{ix+x} dx\]
\[\int e^{x(1+i)} dx\]
\[\frac{ e^{x(1+i)}} {1+i}\]
\[\frac{ e^x e^{1+i} } {1+i}\]
real[\[\frac{ e^x e^{1+i} } {1+i}\]]
\[1/2 e^x sin(x)+1/2 e^x cos(x)\]

Answer 10

hmmmmmm......maybe it sounds a stupid q 4 u...but...whr did e^ix come from? O.o

Answer 11

that is Euler's Formula.

Answer 12

and that technique of using it, and only wanting the real part is boss, very nice job :)

Answer 13

I am addicted to using euler in everything , lol

Answer 14

I would like Euler if only I could say his name, it is apparently pronounced "Oiler"

Answer 15

me too lol, i was using that for some differential equation problems.
@pk51 LOL yeah, its "Oiler"

Answer 16

Ahhhhhhhhhhhhhhhhhhhhhhhhhaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa.........Now i got this..........the problem is tht teacher just gave us the formula of Euler at complex no.s and we never used it.......hmmm......Thnx guys :D

Answer 17

http://stackoverflow.com/questions/1235043/what-latex-editor-do-you-suggest-for-linux

Answer 18

Thanks