TITLE: Integrate : $\int(\sin x+\cos x)^ndx$
QUESTION [7 upvotes]: Problem : $$\int(\sin x+\cos x)^n\ dx$$
I am not getting any clue how to integrate this. Please help . I will be grateful to you. Thanks.

REPLY [11 votes]: Hint: We have 
$$\sin x+\cos x=\sqrt{2}\sin(x+\pi/4).$$
Now use the usual Reduction Formula.