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f-x-ln-x-x-1-e-f-x-x-dx-1-e-ln-f-x-x-dx-




Question Number 933 by 123456 last updated on 29/Apr/15
f(x)=((ln x)/x)  ∫_1 ^e  ((f(x))/x)dx=?   ∫_1 ^e ((ln f(x))/x)dx=?
f(x)=lnxxe1f(x)xdx=?e1lnf(x)xdx=?
Commented by prakash jain last updated on 30/Apr/15
∫ ((ln x)/x^2 ) dx=ln x∙((−1)/x)+∫(1/x^2 ) dx  =−((ln x)/x)−(1/x)  limits from 1 to e,  ((−1)/e)−(1/e)+1=1−(2/e)
lnxx2dx=lnx1x+1x2dx=lnxx1xlimitsfrom1toe,1e1e+1=12e

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