1 ∫(x^(2) -1) / log x dx ???? 0?
1 ∫(x^(2) -1) / log x dx ???? 0?
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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