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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    \[\int_{{}}^{{}}{\frac{\cos 2x+2{{\sin }^{2}}x}{{{\cos }^{2}}x}dx=}\]

    A)            \[2\sec x+c\]

    B)            \[2\tan x+c\]

    C)            \[\tan x+c\]

    D)            None of these

    Correct Answer: C

    Solution :

               \[\int_{{}}^{{}}{\frac{\cos 2x+2{{\sin }^{2}}x}{{{\cos }^{2}}x}\,dx}=\int_{{}}^{{}}{\frac{2({{\cos }^{2}}x+{{\sin }^{2}}x)-1}{{{\cos }^{2}}x}\,dx}\]                                                                       \[=\int_{{}}^{{}}{{{\sec }^{2}}x\,dx}=\tan x+c\].


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