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AP EAMCET · Maths · Indefinite Integration

\(\int \frac{d x}{(x-1) \sqrt{x^2-1}}\) is equal to

  1. A \(-\sqrt{\frac{x-1}{x+1}}+C\)
  2. B \(\sqrt{\frac{x-1}{x^2+1}}+C\)
  3. C \(-\sqrt{\frac{x+1}{x-1}}+C\)
  4. D \(\sqrt{\frac{x^2+1}{x-1}}+C\)
Verified Solution

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, \(\quad d x=\frac{-1}{t^2} d t\)…