a-Evaluate-the-integral-of-the-function-y-x-3x-1-2x-2-2x-3-b-Find-the-constant-A-B-C-in-the-identity-3x-2-ax-x-2a-x-2-a-2-

Question Number 18066 by tawa tawa last updated on 14/Jul/17

(a) Evaluate the integral of the function : y (x) = \frac{3 x + 1}{{2 x}^{2} - 2 x + 3}

(b) Find the constant A, B, C in the identity :

\frac{{3 x}^{2} - ax}{(x - 2 a) (x^{2} + a^{2})} \equiv \frac{A}{(x - 2 a)} + \frac{Bx + Ca}{(x^{2} + a^{2})}

where a is a constant, hence prove that .

\int_{0}^{2} \frac{{3 x}^{2} - ax}{(x - 2 a) (x^{2} + a^{2})} dx = \frac{π}{4} - \frac{3}{2} \ln (2)

Commented by tawa tawa last updated on 15/Jul/17

please help .