let tbe fraction F(x)=(1/(x^n −1)) with n from n and n≥2
1) find the poles of F and decompose it inside C(x)
2)decompose F(x)inside R(x)
3) calculate ∫_2 ^3 F(x)dx .
let f(x) =∫_0 ^∞ ((cos(xcosθ))/(x^2 +θ^2 )) dθ and g(x) =∫_0 ^∞ ((sin(xcosθ))/(x^2 +θ^2 )) dθ
1) find a explicit form of f(x) and g(x)
2) find the value of ∫_0 ^∞ ((cos(2cosθ))/(4+θ^2 )) dθ and ∫_0 ^∞ ((sin(2cosθ))/(4+θ^2 )) dθ
3) let u_n =f(n^2 ) study the serie Σ u_n