The value of  ∫esec⁡x⋅sec3⁡xsin2⁡x+cos⁡x+sin⁡x+sin⁡xcos⁡xdx is

The value of  esecxsec3xsin2x+cosx+sinx+sinxcosxdx is

  1. A

    esecxsec2x+secxtanx+C

  2. B

    esecx+C

  3. C

    esecx(secx+tanx)+C

  4. D

    none of these

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    Solution:

    We have, 

    1=esecxtan2xsecx+sec2x                               +tanxsec2x+tanxsecxdx I=esecx[secxtanx(secx+tanx)                                +secxtanx+sec2xdx

     I=esecxsecxtanxII(secx+tanxI)dx

                                         +esecxsecxtanx+sec2xdx

     I=(secx+tanx)esecxsecxtanx+sec2xesecxdx                                                  +esecxsecxtanx+sec2xdx I=esecx(secx+tanx)+C

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