∫dxx(log⁡x)(log⁡log⁡x)…(log⁡log⁡…⏟8 times x) is equal to

dxx(logx)(loglogx)(loglog8 times x) is equal to

  1. A

    (loglog8 times x)+C

  2. B

    (loglog7 times x)+C

  3. C

    (loglog9 times x)+C

  4. D

    None of these

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    Solution:

    Let   I=dxx(logx)(loglogx)(loglog8 times x)put , (loglog8 times x)=t

    1(loglog7 times x)(loglogx)(logx)xdx=dt I=dtt=logt+C=(logloglog9 times x)+C

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