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Mathematics Worksheet
🧰 Integration Techniques
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Use u-substitution for composite integrands.Use integration by parts: ∫ u dv = uv − ∫ v du.Recognise which technique fits a given integral.Apply both techniques to standard forms.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1∫ 2x(x2 + 3)4 dx (let u = x2 + 3) = ?
2Integration by parts: ∫ u dv = ?
3∫ x sin x dx = ?
4∫ ln x dx (u = ln x, dv = dx) = ?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Integration by parts: ∫ u dv = .
6For ∫ 2x(x2 + 3)4 dx, substitute u = .
7Integrate ∫ 2x(x2 + 3)4 dx using substitution.
8Integrate ∫ x sin x dx using integration by parts.
9Integrate ∫ 5x4(x5 − 2)2 dx using substitution.
🚀 Section C · Challenge ● CHALLENGE 5
10Integrate ∫ ln x dx using integration by parts.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 uv − ∫ v du 6 x2 + 3 7 = (x2 + 3)5/5 + C 8 = −x cos x + sin x + C 9 = (x5 − 2)3/3 + C | 10 = x ln x − x + C