Question

Integrate the following with respect to x.

(3x² - 2x + 5)/((x - 1)(x² + 5))

Answer 1

(3x² - 2x + 5)/((x - 1)(x² + 5)) = A/(x - 1) + (Bx + c)(x² + 5)

⇒ 3x² - 2x + 5 = A(x² + 5) + (Bx + c)(x - 1)  .....(i)

Put x = 1 on both sides (1)