Question 3 - A-Level Maths

Exam Board	AQA
Module	C4 (Core Mathematics 4)
Year	2009
Session	January
Topic	Partial Fractions
Type	Repeated factor with distinct linear factors

1. Express \(\frac { 2 x + 7 } { x + 2 }\) in the form \(A + \frac { B } { x + 2 }\), where \(A\) and \(B\) are integers. (2 marks)
2. Hence find \(\int \frac { 2 x + 7 } { x + 2 } \mathrm {~d} x\).
1. Express \(\frac { 28 + 4 x ^ { 2 } } { ( 1 + 3 x ) ( 5 - x ) ^ { 2 } }\) in the form \(\frac { P } { 1 + 3 x } + \frac { Q } { 5 - x } + \frac { R } { ( 5 - x ) ^ { 2 } }\), where \(P , Q\) and \(R\) are constants.
2. Hence find \(\int \frac { 28 + 4 x ^ { 2 } } { ( 1 + 3 x ) ( 5 - x ) ^ { 2 } } \mathrm {~d} x\).