$\int \frac{\sin x-\cos x}{\sqrt{1-\sin 2 x}} e^{\sin x} \cos x d x$ is equal to
Answer & explanation
Correct answer: option 1
$I=\int e^{\sin x} \cos x d x=e^{\sin x}$
as $1-\sin 2 x=(\sin x-\cos x)^2$
Hence $\int e^{\sin x} \cos x d x$
Put $\sin x=t \Rightarrow \cos x d x=d t$
$\int e^t d t=e^t+c=e^{\sin x}+c$
Hence (1) is the correct answer.