I am trying to show that $\int_{-\pi}^{\pi}e^{\alpha \cos t}\sin(\alpha \sin t)dt=0$
Where $\alpha$ is a real constant.
I found the problem while studying a particular question in this room,this one. It becomes so challenging to me as I am trying to make life easy but I stucked!
EDIT: The integral is from $-\pi$ to $\pi$
EDIT 2: I am sorry for this edit, but it is a typo problem and I fix it now. In my question I have $e^\alpha \cos t$ not $e^\alpha$ only. I am very sorry.