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How to solve Integration of one upon square root of log x

How to solve Integration of one upon square root of log x

Grade:12th pass

1 Answers

Nandana
110 Points
5 years ago
      log(x)=y
      x= e^y
      dx=e^y dy
    ∫ (1/  √y e^y dy  it seems like Gamma function  , which is in the form of  ∫ x^(n-1) e^-x dx
     take y=p
    ∫ 1/ √p e^-p (-dp) = -i ∫ 1/ √p e^-p dp = -i √π  √log x  + C
          where ‘i’ is imaginary part ..
     

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