AP EAMCET · Maths · Indefinite Integration
\(\int \frac{d x}{(x-1) \sqrt{x^2-1}}\) is equal to
- A \(-\sqrt{\frac{x-1}{x+1}}+C\)
- B \(\sqrt{\frac{x-1}{x^2+1}}+C\)
- C \(-\sqrt{\frac{x+1}{x-1}}+C\)
- D \(\sqrt{\frac{x^2+1}{x-1}}+C\)
Answer & Solution
Correct Answer
(C) \(-\sqrt{\frac{x+1}{x-1}}+C\)
Step-by-step Solution
Detailed explanation
Let \(I=\int \frac{d x}{(x-1) \sqrt{x^2-1}}\) Put \(x-1=\frac{1}{t} \Rightarrow x=1+\frac{1}{t}\) Then, \(\quad d x=\frac{-1}{t^2} d t\)…
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