Verified answer

Integrate[ from 4 to t [(−2x) / (9 − x2)^(1/3)] ] = 3/4 (1 - I Sqrt[3]) (7^(2/3) - (-9 + t^2)^(2/3))

As t-> Inf this Integral goes to Infinity

int(-2*x/(9-x^2)^(1/3), x = 4 .. infinity) = - infinity + (infinity*i)*sqrt(3)