A data engineer models the throughput T(x)T(x)T(x) of a high-frequency trading link, measured in terabits per millisecond, as a function of the signal frequency xxx in gigahertz:
T(x)=2x4−13x3+29x2−39x+41(x−3)2,x∈R, x>3 T(x) = \frac{2x^4 - 13x^3 + 29x^2 - 39x + 41}{(x-3)^2}, \quad x \in \mathbb{R}, \; x > 3 T(x)=(x−3)22x4−13x3+29x2−39x+41,x∈R,x>3Determine the values of the constants AAA, BBB, CCC and DDD such that
T(x)=Ax2+Bx+C+D(x−3)2 T(x) = Ax^2 + Bx + C + \frac{D}{(x-3)^2} T(x)=Ax2+Bx+C+(x−3)2DHence find
∫T(x) dx \int T(x) \, dx ∫T(x)dx
