integrate logx dx/(1+logx)(1+logx)

Asked by  | 14th Feb, 2012, 01:58: PM

Expert Answer:

Let logx = t , x = et , dx = et . dt
I = Integration et . t/(1+t)2 .dt
= Int. et  { (t + 1 - 1)/(1+t)2 } = Int. et { 1/(1+t) - 1/(1+t)2 } = et . 1/(1+t) + C
Using Int. ex(f(x) + f'(x)) = exf(x) + C
I = x/(1+logx) + C

Answered by  | 14th Feb, 2012, 03:17: PM

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