let f(x) =∫_(π/3) ^(π/2) (dθ/(1+xtanθ)) with x real
1) find a explicit form for f(x)
2) determine also g(x) =∫_(π/3) ^(π/2) ((tanθ)/((1+xtanθ)^2 )) dθ
3) let U_n (x) =f^((n)) (x) give U_n (x) at form of integral.
4) calculate ∫_(π/3) ^(π/2) (dθ/(1+2tanθ)) and ∫_(π/3) ^(π/2) ((tanθ dθ)/((1+2tanθ)^2 ))