JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int \sin ^{-1}\left(\sqrt{\frac{x}{1+x}}\right) d x=A(x) \tan ^{-1}(\sqrt{x})+B(x)+C\) where \(C\) is a constant of integration, then the ordered pair \(( A ( x ), B ( x ))\) can be
- A \((x-1, \sqrt{x})\)
- B \((x+1, \sqrt{x})\)
- C \((x+1,-\sqrt{x})\)
- D \((x-1,-\sqrt{x})\)
Answer & Solution
Correct Answer
(C) \((x+1,-\sqrt{x})\)
Step-by-step Solution
Detailed explanation
Put \(x=\tan ^{2} \theta \Rightarrow d x=2 \tan \theta \sec ^{2} \theta d \theta\) \(\int \theta \cdot\left(2 \tan \theta \cdot \sec ^{2} \theta\right) d \theta\) \(\downarrow \downarrow\) I I \(\quad\) (By parts) \(=\theta \cdot \tan ^{2} \theta-\int \tan ^{2} \theta d \theta\)…
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