Edexcel P3 2022 June — Question 3

Exam BoardEdexcel
ModuleP3 (Pure Mathematics 3)
Year2022
SessionJune
TopicIntegration by Substitution

3. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable.
Given that \(k\) is a positive constant,
  1. find $$\int \frac { 9 x } { 3 x ^ { 2 } + k } d x$$ Given also that $$\int _ { 2 } ^ { 5 } \frac { 9 x } { 3 x ^ { 2 } + k } \mathrm {~d} x = \ln 8$$
  2. find the value of \(k\)