| Exam Board | Edexcel |
| Module | FP3 (Further Pure Mathematics 3) |
| Topic | Integration using inverse trig and hyperbolic functions |
3. Using the substitution \(\mathrm { x } = \frac { 3 } { \sinh \theta }\), or otherwise, find the exact value of
$$\int _ { 4 } ^ { 3 \sqrt { } 3 } \frac { 1 } { x \sqrt { } \left( x ^ { 2 } + 9 \right) } d x$$
giving your answer in the form a ln b , where a and b are rational numbers.
(Total 8 marks)