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JEE Main & Advanced Mathematics Indefinite Integrals Question Bank Fundamental Integration

  • question_answer
    \[\int_{{}}^{{}}{{{(\sec x+\tan x)}^{2}}dx=}\]              [MP PET 1987, 92]

    A)            \[2(\sec x+\tan x)-x+c\]

    B)            \[1/3{{(\sec x+\tan x)}^{3}}+c\]

    C)            \[\sec x(\sec x+\tan x)+c\]

    D)            \[2(\sec x+\tan x)+c\]

    Correct Answer: A

    Solution :

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


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