Question 3 - A-Level Maths

Exam Board	AQA
Module	C3 (Core Mathematics 3)
Year	2012
Session	January
Topic	Standard Integrals and Reverse Chain Rule

Given that \(y = 4 x ^ { 3 } - 6 x + 1\), find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\).
(l mark)
Hence find \(\int _ { 2 } ^ { 3 } \frac { 2 x ^ { 2 } - 1 } { 4 x ^ { 3 } - 6 x + 1 } \mathrm {~d} x\), giving your answer in the form \(p \ln q\), where \(p\) and \(q\) are rational numbers.