-\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