Question 4 - A-Level Maths

Exam Board	AQA
Module	C4 (Core Mathematics 4)
Year	2007
Session	January
Topic	Partial Fractions
Type	Partial fractions with algebraic division first

1. Express \(\frac { 3 x - 5 } { x - 3 }\) in the form \(A + \frac { B } { x - 3 }\), where \(A\) and \(B\) are integers. (2 marks)
2. Hence find \(\int \frac { 3 x - 5 } { x - 3 } \mathrm {~d} x\).
  (2 marks)
1. Express \(\frac { 6 x - 5 } { 4 x ^ { 2 } - 25 }\) in the form \(\frac { P } { 2 x + 5 } + \frac { Q } { 2 x - 5 }\), where \(P\) and \(Q\) are integers.
  (3 marks)
2. Hence find \(\int \frac { 6 x - 5 } { 4 x ^ { 2 } - 25 } \mathrm {~d} x\).