∫{1+2tan⁡x(tan⁡x+sec⁡x)}1/2dx   is equal 

{1+2tanx(tanx+secx)}1/2dx   is equal 

  1. A

    logsecx(secxtanx)+C

  2. B

    logcosec(secx+tanx)+C

  3. C

    logsecx(secx+tanx)+C

  4. D

    log(secx+tanx)+C

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    Solution:

     We have, 

     I={1+2tanx(tanx+secx)}1/2dx I=1+tan2x+tan2x+2tanxsecx1/2dx I=sec2x+tan2x+2tanxsecx1/2dx

     I    =(tanx+secx)dx I    =logsecx+log(secx+tanx)+C I    =logsecx(secx+tanx)+C

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