$\smallint \,\,\frac{{{x^2} - \,\,2}}{{{x^3}\,\sqrt {{x^2} - \,\,1} }}\;\,\,dx$ is equal to

$\frac{{{x^2}}}{{\sqrt {{x^2} - \,\,1} }}\, + c$

$ - \,\,\frac{{{x^2}}}{{\sqrt {{x^2} - \,\,1} }}\, + \,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\frac{{{x^2} - \,\,2}}{{{x^3}\,\sqrt {{x^2} - \,\,1} }}\;\,\,dx

is equal to

View answer and explanation

Correct option: D

- \,\,\frac{{\sqrt {{x^2} - \,\,1} }}{{{x^2}}}\, + \,c

Option D (

\ - \,\,\frac{{\sqrt {{{{x^2} - \,\,1}}} }}{{{{x^2}}}}\, + \,\,c

) is correct because after trigonometric substitution and simplification, the result matches this option.