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Evaluate: int0^(2pi)cos^5x\ dx...

Evaluate: `int_0^(2pi)cos^5x\ dx`

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`int_(0)^(2pi) cos^(5) x dx = 2 int_(0)^(pi) cos^(5) x dx`
`[ :' int_(0)^(2a) f(x) =2int_(0)^(a) f(x) dx , " where " f(2a -x) =f(x)`
`:. cos^(5) (2pi-x)=cos^(5) x]`
`=2xx0=0`
`( :' int_(0)^(2a)f(x) =0 " if " f(2a-x)=-f(x),`
`" Here " 2a=pi , :. cos^(5) (pi-x) =-cos^(5) x)`
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