| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Topic | Integration by Parts |
| Type | Integration of ln(x) alone |
| Difficulty | Standard +0.3 This is a straightforward integration problem using a given substitution. The substitution x = e^u simplifies (ln x)^2 to u^2, and dx = e^u du. Students then integrate u^2 e^u using integration by parts twice (standard technique), before substituting back. While it requires multiple steps, the substitution is provided and the technique is routine for Further Maths students. |
| Spec | 4.08h Integration: inverse trig/hyperbolic substitutions |
8. Using the substitution $x = \mathrm { e } ^ { u }$, find $\int ( \ln x ) ^ { 2 } \mathrm {~d} x$.\\[0pt]
\\
\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q8 [6]}}