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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 18

  • question_answer
    \[{{\int{\left\{ 1+2\tan x(\tan x+\sec x) \right\}}}^{1/2}}dx\] is equal to

    A) \[\log \,\sec \,x(\sec x-\tan x)+C\]

    B) \[\log \,cosec\,x(\sec x+\tan x)+C\]

    C) \[\log \,sec\,x(\sec x+\tan x)+C\]

    D) \[\log \,(\sec x+\tan x)+C\]

    Correct Answer: C

    Solution :

    \[{{\int{\left\{ 1+2{{\tan }^{2}}x+2\tan x\sec x \right\}}}^{\frac{1}{2}}}dx\] \[=\int{{{({{\sec }^{2}}x+{{\tan }^{2}}x+2\tan x\sec x)}^{\frac{1}{2}}}dx}\] \[=\int{(\sec x+\tan x)dx=\log \sec x(\sec x+\tan x)+C}\]


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