Question Number 100829 by  M±th+et+s last updated on 28/Jun/20

hello every one     prove that  ∫_0 ^(π/2) cos^u (x) cos(ax) arctan(b cos(x)) dx  =((2^(−u−2) .π.b.Γ(u+2))/(Γ(((u−a+3)/2))Γ(((u+a+3)/2)))).x_4 F_3  ((((1/2),1+(u/2),((u+3)/2),−b^2 )),(((3/2),((u−a+3)/2),((u+a+3)/2))) )      Re u>−1 ,∣arg(1+b^2 ) ∣<π