| Exam Board | Edexcel |
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2013 |
| Session | June |
| Topic | Integration using inverse trig and hyperbolic functions |
2. (a) Find
$$\int \frac { 1 } { \sqrt { } \left( 4 x ^ { 2 } + 9 \right) } d x$$
(b) Use your answer to part (a) to find the exact value of
$$\int _ { - 3 } ^ { 3 } \frac { 1 } { \sqrt { \left( 4 x ^ { 2 } + 9 \right) } } d x$$
giving your answer in the form \(k \ln ( a + b \sqrt { } 5 )\), where \(a\) and \(b\) are integers and \(k\) is a constant.