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

$\frac{2}{3}\,\,{\sin ^{ - 1}}\left( {{{\cos }^{3/2}}\,\,x} \right) + C$

$\frac{3}{2}\,\,{\sin ^{ - 1}}\left( {{{\cos }^{3/2}}\,\,x} \right) + C$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

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

is equal to

View answer and explanation

Correct option: C

\frac{2}{3}\,\,{\cos ^{ - 1}}\,\,\left( {{{\cos }^{3/2}}\,\,x} \right) + C

Option C (

\frac{2}{3}\\,{\cos ^{ - 1}}\\,\left( {{{{

\cos

}}^{3/2}}\\,x} \right) + C

) is correct because it represents the result of the integration after simplification and substitution.