Let's consider the integrer:
Let's assume that:
then our interger:
next:
oraz
and finally we get:
so:
...and I am not sure if that solution is correct.
-\int cos(2x)e^{cos(x)+sin(x)}=e^{cos(x)+sin(x)} \Big (cos(x)+sin(x)+1 \Big) +c " alt="-\int cos(2x)e^{cos(x)+sin(x)}=e^{cos(x)+sin(x)} \Big (cos(x)+sin(x)+1 \Big) +c " />
you should just change the red signs negative to positive and the positive to the negative
you answer is correct
and this come from
sinx derive is cos and cosx derive -sinx
look carefully to this