| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Integration using inverse trig and hyperbolic functions |
| Type | Derivative of inverse hyperbolic function |
| Difficulty | Challenging +1.2 Part (a) is a standard FP3 proof requiring the chain rule and implicit differentiation of y = tanh^{-1}(x), which is bookwork. Part (b) requires integration by parts with an inverse hyperbolic function, which is a step beyond routine but follows a predictable pattern once the derivative from (a) is known. This is moderately challenging for Further Maths students but represents expected FP3 content rather than requiring novel insight. |
| Spec | 1.08i Integration by parts4.07f Inverse hyperbolic: logarithmic forms |
\begin{enumerate}[label=(\alph*)]
\item Prove that the derivative of $\operatorname{artanh} x$, $-1 < x < 1$, is $\frac{1}{1-x^2}$. [3]
\item Find $\int \operatorname{artanh} x \, dx$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q11 [7]}}