(i)[3]
Evaluate $\int \frac{\ln x}{x^3}\, dx$.
(ii)[2]
Hence demonstrate that $\int_{1}^{2} \frac{\ln x}{x^3}\, dx = \frac{1}{16}(3 - \ln 4)$.
Mathematics 9709 · AS & A Level · Integration
Integration — practice question
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply integration by parts to get an expression of the form $a\frac{\ln x}{x^2}+b\int \frac{1}{x}\cdot\frac{1}{x^2}\,dx$.” …
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