1 ∫(x^(2) -1) / log x dx ???? 0?

Posted on 2016-03-26 14:23:00 in Math by DEVAJITH

it can done easily by calculating the integral 
1 
I=∫(x^(n) -1) / log x dx 
0 
then 
dI/dn= d/dn.(x^n-1)/log(x) dx =x^n.log(x)/log(x) = x^n dx. 

∫ x^n dx = (x^(n+1)/(n+1)). 
applying limits x=0 to 1 we get 1/(n+1). 
dI/dn = 1/(n+1) 
therefore I=∫dn/(n+1)= log(n+1) 

constant of integration is 0 as we substitute n=0 in the 1st equation 

therefore I=log(n+1) 
Therefore the answer is log(3) 

i know it is not a straight way 
I just wanted to know if there were other methods????

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