Question

\(\smallint \frac{{{x^2} - 1}}{{{x^4} - 1}}dx = ?\)
1. tan^-1 x + c
2. sin^-1 x + c
3. cot^-1 x + c
4. \(\frac{1}{2}\log \left| {\frac{{x - 1}}{{x + 1}}} \right| + c\)
5. sec-1 x + c

Answer 1

Correct Answer - Option 1 : tan^-1 x + c

Concept:

\(\smallint \frac{1}{{{x^2} + 1}} = {\tan ^{ - 1}}x + c\;\)

Calculation:

\(\smallint \frac{{{x^2} - 1}}{{{x^4} - 1}}dx\)

\(= \smallint \frac{{{x^2} - 1}}{{\left( {{x^2} - 1} \right)\left( {{x^2} + 1} \right)}}dx\)

\(= \smallint \frac{1}{{{x^2} + 1}}dx\)

= tan^-1 x + c