∫1sin6⁡x+cos6⁡xdx is equal to

1sin6x+cos6xdx is equal to

  1. A

    tan1(tanx+cotx)+C

  2. B

    tan1(cotxtanx)+C

  3. C

    tan1(tanxcotx)+C

  4. D

    none of these

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    Solution:

    Let

        I=1sin6x+cos6xdx=sec6x1+tan6xdx I=1+tan2x21+tan6xsec2xdx

                     =1+t221+t6dt, where t=tanx

          I=t2+1t41t2+1dt=1+1t2t2+1t21dt=dt1tt1t2+12 I=tan1t1t+C=tan1(tanxcotx)+C

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