$\int \sin ^{-1}\left(\sqrt{\frac{x}{a+x}}\right) d x=$

• A

  $(a+x) \operatorname{Tan}^{-1} \sqrt{\frac{x}{a}}+a x+c$
• B

  $(a+x) \operatorname{Tan}^{-1} \sqrt{\frac{x}{a}}+\sqrt{a x}+c$
• C

  $(a+x) \operatorname{Tan}^{-1} \sqrt{\frac{a}{x}}-\sqrt{a x}+c$
• Correct answer
  D

  $(a+x) \operatorname{Tan}^{-1} \sqrt{\frac{x}{a}}-\sqrt{a x}+c$

Hence, the correct answer is option: 'D'.