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

Compute the integrals: int_(oo)f(x^(n)+x^(-n))log x(dx)/(1+x^(2))0

Compute the integral int_(0)^(1) xe^(x) dx

Compute the integrals : int (x - 1)e^(-x) dx

compute the integral : int_(1)^(2) (dx)/(x)

Compute the integrals : int_(0)^(1) x "arc tan x dx

Compute the integrals : (a) int_(0)^(pi//2) (cos x dx)/( 6 - 5 sin x + sin^(2) x) (b) int _(0)^(pi//2) (dx)/( 2 + cos x)