If ∫  cot2tan−11+x−x1/41+x+x1/4dx=qxp/qp+C (where p and q are relatively prime and C is constant of integration), then which of the following option(s) is / are correct ?

let θ= 1+x−x1+x+x               =1+x−x21+x−x  rationalise the denominator=1+x−x   now given integrand =cot 2 tan-1θ=1tan2tan-1θ=1-θ22θ  =  1−1+x+x−2x+x21+x−x =−2x+2x1+x21+x−x=2x1+x−x21+x−x⇒I=∫  xdx=∫  x1/4dx = 45x54+c