$\int \large\frac{x^{49} \tan^{-1} (x^{50})}{(1+x^{100})}$$dx=k(\tan^{-1}(x^{50})^2+c$ then k is equal to :

Question

\[\begin {array} {1 1} (a)\;\frac{1}{50} & \quad (b)\;-\frac{1}{50} \\ (c)\;\frac{1}{100} & \quad (d)\;-\frac{1}{100} \end {array}\]