Question: can maple give answer for int(cos(x)^n,x) ?

Was trying to see if I can get the reduction formulas for int(cos(x)^n,x) in maple. But it seems no assumption used can make Maple give any result for this.  Mathematica gives a result using Hypergeometric2F1 (even with no assumption on n, which I am not sure about now), but was wondering why maple can't do this one:


int( (cos(x))^n,x) assuming n::integer;

int( (cos(x))^n,x) assuming n::posint;

In Mathematica, I get:

I am newbie in Maple, so may be I am missing some command or doing something wrong.

ps. I was trying to obtain

But this is lost case now. I just need to find out first why int(cos(x)^n,x) does not evaluate to anything in Maple.

fyi, the Hypergeometric result for $\int cos^n(x) \,dx$ can be seen in this reference (half way down the page):

ps. can't one enter Latex in this forum like at stack exchange?



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