$\large\int \bigg(\sqrt {\large\frac{a+x}{a-x}}+\sqrt {\large\frac{a-x}{a+x}}\bigg)$$dx= $

Question

\[\begin {array} {1 1} (a)\;2 \sin ^{-1} \bigg(\frac{x}{a}\bigg)+c & \quad (b)\; 2a \sin ^{-1} \bigg(\frac{x}{a}\bigg)+c \\ (c)\;2 \cos ^{-1} \bigg(\frac{x}{a}\bigg)+c & \quad (d)\;2a \cos ^{-1} \bigg(\frac{x}{a}\bigg)+c \end {array}\]