OCR C4 — Question 5

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
TopicPartial Fractions
TypeRepeated factor with distinct linear factors

5. $$f ( x ) = \frac { 7 + 3 x + 2 x ^ { 2 } } { ( 1 - 2 x ) ( 1 + x ) ^ { 2 } } , \quad | x | > \frac { 1 } { 2 }$$
  1. Express \(\mathrm { f } ( x )\) in partial fractions.
  2. Show that $$\int _ { 1 } ^ { 2 } \mathrm { f } ( x ) \mathrm { d } x = p - \ln q$$ where \(p\) is rational and \(q\) is an integer.