Question

Integrate this

Answer 1

\[\Huge \int\limits_{}^{} \frac{\sin x}{\sin x+\cos x}\]

Answer 2

I tried converting sinx to 2tanx/2 / (1+tan^2 x/2) and cosx to 1-tan^2x/2 / 1+tan^2 x/2 but it lead me nowhere..need a hint :(

Answer 3

@amistre64 @dan815 @ganeshie8 @yrelhan4

Answer 4

let \[A=\int \frac{\sin x}{\sin x + \cos x}dx\\B=\int\frac{\cos x}{\sin x + \cos x}dx\]

evaluate B+A and B-A

Answer 5

\[\large B+A=\int\frac{\sin x + \cos x}{\sin x + \cos x}dx = x\]
\[\large B-A=\int\frac{\cos x - \sin x}{\sin x + \cos x}dx =\ln|\sin x + \cos x|\]
subtract the two equations

Answer 6

\[\frac{ 1 }{ 2 } \int\limits_{}^{}\frac{ \sin(x)+\cos(x)+\sin(x)-\cos(x) }{ \sin(x)+\cos(x) }=\frac{ 1 }{ 2 } \int\limits_{}^{}1+\frac{ \sin(x)-\cos(x) }{ \sin(x)+\cos(x) }=\frac{ 1 }{ 2 }(x-\ln(\sin(x)+\cos(x)))\]

Answer 7

sorry @sirm3d I did not see your reply

Answer 8

I don't even know where I'm going with this.. @sirm3d 's looks so blissfully elegant :D

Answer 9

that was nice @sirm3d

Answer 10

thank you. but credit goes to Schaum's Outline Series. hehehe.

Answer 11

thanks!