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AP EAMCET · Maths · Indefinite Integration

\(\int \frac{x^2-2}{x^3 \sqrt{x^2-1}} d x=\)

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

Answer & Solution

Correct Answer

(D) \(\frac{-\sqrt{x^2-1}}{x^2}\)

Step-by-step Solution

Detailed explanation

\(u=\sqrt{x^2-1}\) \(d u=\frac{1}{\not z}\) \(\left(x^2-1\right)^{1 / 2-1} \not2 x\) \(d_x\) \(=\frac{x}{\sqrt{x^2-1}} d x\) \(d x=\frac{\sqrt{x^2-1}}{x} d u\) \(\begin{aligned} & u=\sqrt{x^2-1} \\ & x^2-1=u^2\end{aligned}\)…