OCR C4 Specimen — Question 8

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
SessionSpecimen
TopicPartial Fractions
TypeIntegration with substitution and partial fractions

8 Let \(I = \int \frac { 1 } { x ( 1 + \sqrt { } x ) ^ { 2 } } \mathrm {~d} x\).
  1. Show that the substitution \(u = \sqrt { } x\) transforms \(I\) to \(\int \frac { 2 } { u ( 1 + u ) ^ { 2 } } \mathrm {~d} u\).
  2. Express \(\frac { 2 } { u ( 1 + u ) ^ { 2 } }\) in the form \(\frac { A } { u } + \frac { B } { 1 + u } + \frac { C } { ( 1 + u ) ^ { 2 } }\).
  3. Hence find \(I\).