Edexcel FP3 2012 June — Question 5

Exam BoardEdexcel
ModuleFP3 (Further Pure Mathematics 3)
Year2012
SessionJune
TopicHyperbolic functions

  1. (a) Differentiate \(x \operatorname { arsinh } 2 x\) with respect to \(x\).
    (b) Hence, or otherwise, find the exact value of
$$\int _ { 0 } ^ { \sqrt { 2 } } \operatorname { arsinh } 2 x \mathrm {~d} x$$ giving your answer in the form \(A \ln B + C\), where \(A , B\) and \(C\) are real.