Question

Integral (sinx +cos x/(e^-x+sin x))

Answer 1

can i form to this//
\[\int\limits \frac{ \cos 2x }{ cox-sinx } *\frac{ 1 }{ e^{x}sinx+1 }\]

Answer 2

is this the problem? \[\Large \int\limits \left(\frac{\sin x + \cos x}{e^{-x}+\sin x}\right)dx\]

Answer 3

yes..

Answer 4

start by multplying top and bottom by \(e^x\)

Answer 5

so it will be integral (sinx +cos x)/(1+e^xsin x)

Answer 6

\[\Large \frac{ e^x \sin x + e^x \cos x}{ 1+e^x \sin x }\]

Answer 7

ok..then???

Answer 8

let \(\displaystyle \large u = 1 + e^x \sin x\)

Answer 9

\(\Large du = ?\)

Answer 10

du=\[e^x \sin x +e^x \cos x \]

Answer 11

so the answer is \[\ln\left| 1+e^x sinx \right|\]

Answer 12

right

Answer 13

ok thank>>

Answer 14

you're welcome.