AP EAMCET · Maths · Indefinite Integration
If \(\quad \int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x=f(x)-\log \left(1+x^2\right)\) then \(f(x)\) is equal to
- A \(2 x \tan ^{-1} x\)
- B \(-2 x \tan ^{-1} x\)
- C \(x \tan ^{-1} x\)
- D \(-x \tan ^{-1} x\)
Answer & Solution
Correct Answer
(A) \(2 x \tan ^{-1} x\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \sin ^{-1}\left(\frac{2 x}{1+x^2}\right) d x\) Put \(x=\tan \theta \Rightarrow d x=\sec ^2 \theta d \theta\)…
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