Compute the integrals: `int_0^oof(x^n+x^(-n))logx(dx)/x`

Explanation

Here limits (reciprocal) and type of functions (reciprocal terms are present i.e. `x` and `1//x`) suggest that we must substitute `1//t` for `x`.
Let `t=1//x` or `x=1//t`. So `dx=-1/(t^(2))dt`.
Also when `xto 0, t to oo` when `xto oo, t to 0`. Thus,
`I=int_(0)^(oo) f(x^(n)+x^(-n)) In x(dx)/x`
`=int_(oo)^(0)f(t^(-n)+t^(n))In(1/t)(-(dt)/(t^(2)))/(1/t)`
`=-int_(0)^(oo) ft^(n)+t^(-n)In(t)(dt)/t`
`=-1`
or `2I=0` or `I=0`