$\smallint \,\,\frac{{{x^4} + 1}}{{{{\left( {1 - {x^4}} \right)}^{3/2}}}}\,\,dx$ is equal to

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

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\frac{{{x^4} + 1}}{{{{\left( {1 - {x^4}} \right)}^{3/2}}}}\,\,dx

is equal to

View answer and explanation

Correct option: A

\frac{x}{{\sqrt {1\,\, - \,\,{x^4}} }}\,\, + \,\,C

Option A (

\frac{x}{{\sqrt {1\,\, - \,\,{x^4}} }}\,\, + \,\,C

) is correct because the integral can be solved by rewriting the expression and using a suitable substitution.