Q3. (7 marks) Determine the condition that the constants a, b, and c should satisfy in order that the following integral is a rational function: ax2 + bat c 2c3 (x - 1)2 -dx. Hint: the statement that the following integral is a rational function means: ax2 + bat c P (x) 23 ( x - 1)2 d = Q (x) + C, 1where P (x) and Q (x) are polynomial functions. In other words, the result of integra- tion does not contain transcendental functions like logarithms, trigonometric and inverse trigonometric functions, etc