Standard +0.3 This is a straightforward integration by parts question with a standard form (x^n·ln(x)). Students need to recognize the technique, apply it correctly with u=ln(x) and dv=32x^(-5)dx, then integrate the resulting simpler expression. It's slightly above average difficulty due to the negative power and requiring careful algebraic manipulation, but it's a textbook-style question with no novel insight required.
\(k\frac{x^{-4}}{-4}\ln x - \int k\frac{x^{-4}}{-4} \times \frac{1}{x}\,dx\) oe
M1
Allow sign errors only
\([32]\frac{x^{-4}}{-4}\ln x - \int[32]\frac{x^{-4}}{-4} \times \frac{1}{x}\,dx\) oe
A1
All correct
\(-8x^{-4}\ln x - 2x^{-4} + c\) oe isw
A1 A1 [4]
Two of three elements correct; all three elements correct
## Question 6:
$k\frac{x^{-4}}{-4}\ln x - \int k\frac{x^{-4}}{-4} \times \frac{1}{x}\,dx$ oe | **M1** | Allow sign errors only
$[32]\frac{x^{-4}}{-4}\ln x - \int[32]\frac{x^{-4}}{-4} \times \frac{1}{x}\,dx$ oe | **A1** | All correct
$-8x^{-4}\ln x - 2x^{-4} + c$ oe isw | **A1 A1 [4]** | Two of three elements correct; all three elements correct
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6 Find $\int \frac { 32 } { x ^ { 5 } } \ln x \mathrm {~d} x$.
Answer all the questions\\
Section B (78 marks)
\hfill \mbox{\textit{OCR MEI Paper 2 2019 Q6 [4]}}