| Exam Board | AQA |
|---|
| Module | C3 (Core Mathematics 3) |
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| Topic | Integration by Parts |
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10
- By writing \(\ln x\) as \(( \ln x ) \times 1\), use integration by parts to find \(\int \ln x \mathrm {~d} x\).
- Find \(\int ( \ln x ) ^ { 2 } \mathrm {~d} x\).
- Use the substitution \(u = \sqrt { x }\) to find the exact value of
$$\int _ { 1 } ^ { 4 } \frac { 1 } { x + \sqrt { x } } \mathrm {~d} x$$
(7 marks)