| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Standard integral of 1/√(x²+a²) |
| Difficulty | Challenging +1.2 This is a standard Further Maths integration question requiring completion of the square to get the form 1/√(u² + a²), then applying the inverse hyperbolic sine (or logarithmic equivalent) formula. While it requires knowledge of a specialized technique beyond A-level, it's a routine textbook exercise for FP3 students with no novel problem-solving required—just methodical application of the standard method. |
| Spec | 1.08h Integration by substitution |
Evaluate $\int_1^4 \frac{1}{\sqrt{x^2 - 2x + 17}} \, dx$, giving your answer as an exact logarithm. [5]
\hfill \mbox{\textit{Edexcel FP3 Q38 [5]}}