AP EAMCET · Maths · Indefinite Integration
\(\int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x=\)
- A \((a+x) \tan ^{-1} \sqrt{\frac{x}{a}}-\sqrt{a x}+c\)
- B \(\frac{1}{a+x} \tan ^{-1}\left(\frac{x}{a}\right)-\sqrt{a x}+c\)
- C \((a+x) \tan ^{-1}\left(\frac{a}{x}\right)+\sqrt{a x}+c\)
- D \(\sqrt{a+x} \tan ^{-1}\left(\frac{x}{a}\right)+a x+c\)
Answer & Solution
Correct Answer
(A) \((a+x) \tan ^{-1} \sqrt{\frac{x}{a}}-\sqrt{a x}+c\)
Step-by-step Solution
Detailed explanation
\(\mathrm{I}=\int \sin ^{-1} \sqrt{\frac{x}{a+x}} d x\)…
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