Question 1 - A-Level Maths

Exam Board	AQA
Module	C4 (Core Mathematics 4)
Year	2012
Session	June
Topic	Partial Fractions
Type	Partial fractions with algebraic division first

1. Express $\frac { 5 x - 6 } { x ( x - 3 ) }$ in the form $\frac { A } { x } + \frac { B } { x - 3 }$.
  (2 marks)
2. Find $\int \frac { 5 x - 6 } { x ( x - 3 ) } \mathrm { d } x$.
  (2 marks)
1. Given that $$4 x ^ { 3 } + 5 x - 2 = ( 2 x + 1 ) \left( 2 x ^ { 2 } + p x + q \right) + r$$ find the values of the constants $p , q$ and $r$.
2. Find $\int \frac { 4 x ^ { 3 } + 5 x - 2 } { 2 x + 1 } \mathrm {~d} x$.