Integrate : $ \int \cos^{-1} \sqrt {\large\frac{x}{a+x}}$$dx$

Question

$(a)\;\frac{\pi}{2} x -\frac{x}{2a} \sqrt {\frac{x}{a}}+\frac{1}{2} \sqrt {\frac{x}{a}}-\frac{1}{2} \tan ^{-1} (\sqrt{\frac{x}{a}})+c \\(b)\;\frac{\pi}{2} x -\frac{x}{2a} \sqrt {\frac{x}{a}}+\frac{1}{2} \sqrt {\frac{x}{a}}-\frac{1}{2} \cot ^{-1} (\sqrt{\frac{x}{a}})+c \\(c)\; \frac{\pi}{2} x -\frac{x}{2a} \sqrt {\frac{x}{a}}+\frac{1}{2} \sqrt {\frac{x}{a}}-\frac{1}{2} \sin ^{-1} (\sqrt{\frac{x}{a}})+c \\ (d)\;\frac{\pi}{2} x -\frac{x^2}{2a} \sqrt {\frac{x}{a}}+\frac{x}{2} \sqrt {\frac{x}{a}}-\frac{1}{7} \tan ^{-1} (\sqrt{\frac{x}{a}})+c$