let f(x) =∫_0 ^∞ ((sin(t^2 ))/((x^2 +t^2 )^2 ))dt with x>0
1)determine a explicit form for f(x)
2) find also g(x) =∫_0 ^∞ ((sin(t^2 ))/((x^2 +t^2 )^3 ))dt
3) give f^((n)) (x) at form of integral and calculate f^((n)) (1).
4) find the valueof ∫_0 ^∞ ((sin(t^2 ))/((1+t^2 )^2 )) dt and ∫_0 ^∞ ((sin(t^2 ))/((1+t^2 )^3 ))dt