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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    \[\int_{{}}^{{}}{\frac{dx}{4{{\cos }^{3}}2x-3\cos 2x}}=\]

    A)            \[\frac{1}{3}\log [\sec 6x+\tan 6x]+c\]

    B)            \[\frac{1}{6}\log [\sec 6x+\tan 6x]+c\]

    C)            \[\log [\sec 6x+\tan 6x]+c\]

    D)            None of these

    Correct Answer: B

    Solution :

               \[\int_{{}}^{{}}{\frac{dx}{4{{\cos }^{3}}2x-3\cos 2x}}=\int_{{}}^{{}}{\frac{dx}{\cos 6x}=\int_{{}}^{{}}{\sec 6xdx}}\]                                                                        \[=\frac{1}{6}\log \,(\sec 6x+\tan 6x)+c.\]


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