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The value of ∫(1/lnX ) dx on limits 0 to 1 is......

  1. The value of ∫(1/lnX ) dx on limits 0 to 1 is......

Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago
 

I=∫(1/lnx)dx

let lnx =t

     or x= et

        dx =etdt

I =∫(1/t) etdt

  =∫(1/t)[1+t+t2/2! + t3/3! +..........]dt

  =∫[1/t +1+t/2! + t2/3! +..........]dt

  =lnt + t + t2/2*2! + t3/3* 3! +.........

  =ln(lnx) + lnx + (lnx)2/2*2! + (lnx)3/3* 3! +.........

  =ln(lnx) +  ∑(lnx)r/r*r!  where r varies from 1 to infinity

 

now put the limit

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