$\smallint \,\,\frac{{{x^4} - \,\,1}}{{{x^2}\,\sqrt {{x^4} + \,\,{x^2} + 1} }}\,\,dx$ is equal to

$\frac{x}{{\sqrt {{x^4} + {x^2} + 1} }} + C$

$\frac{{2x}}{{\sqrt {{x^4} + {x^2} + 1} }} + C$

$\frac{{\sqrt {{x^4} + {x^2} + 1} }}{{2x}} + C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

\int \,\,\frac{{{x^4} - \,\,1}}{{{x^2}\,\sqrt {{x^4} + \,\,{x^2} + 1} }}\,\,dx

is equal to

View answer and explanation

Correct option: B

\frac{{\sqrt {{x^4} + {x^2} + 1} }}{x} + C

Option B (

\frac{{\sqrt {{x^4} + {x^2} + 1} }}{x} + C

) is correct because after simplifying and integrating the given expression, the result matches this form.