How Do You Integrate sin(2x) e^(sin x)?

[biogoal123]

hey guys I am absolutely stumped on this one integration problem:

it asks us to integrate sin (2x) e ^ (sin x)

i integrated by parts once and was left with an even larger term to integrate, which leads me to believe that i might be doing it wrong

any help is appreciated, thanks

 

[Whitishcube]

Try expanding sin(2x) using a double angle formula.

 

[biogoal123]

wow ok i feel like an idiot. when i split it into double angles i had (2 sin cos e^sin) and i kept having my two terms for integration by parts being (cos sin) and (e ^ sin) instead of the VERY OBVIOUS one which i kept missing which was (sin) and (cos e ^sin) which gave a very nice and smooth integration

thanks again

 

[adriank]

You could also have done a substitution u = sin x.