What is the antiderivative of (sin 2x)e^cos2x?

Question

(-1/2)e^-cos2x + C ?

(1/2)e^-sin2x + C ?

Answer 1

neither
it is -1/2 e^cos 2x + C

to confirm differentiate the result and find itr

if you need to integate let cos 2x = y
then -2 sin 2x dx = dy
sin 2x dx = -dy/2

put the value we need to integrate - e^y dy/2
result = - e^y/2 + C
= -1/2e^(cos 2x) + C

Answer 2

(-1/2)e^cos2x+C

Answer 3

first one !!
it's quite obvious!