ClearAll[se, so]

sinIntegral[n_, r_] := Integrate[ Sin[x]^n, {x,0,r}] ;
cosIntegral[n_, r_] := Integrate[ Cos[x]^n, {x,0,r}] ;

sinIntegral[#, Pi/2] &/@ Range[7] 
cosIntegral[#, Pi/2] &/@ Range[7] 

sinIntegral[#, Pi] &/@ Range[7] 
cosIntegral[#, Pi] &/@ Range[7]