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A2 Unit 3 Pure Mathematics B

Quick questions on Integration: by parts, by substitution and partial fractions - WJEC A-Level Maths

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is integration by substitution?
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Substitution reverses the chain rule. Choose a new variable uu (often the inside of a composite function), differentiate to get dudx\dfrac{du}{dx}, and replace both the function and dxdx so the integral is entirely in uu.
What are integration by parts?
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By parts reverses the product rule and is used for products like xexx\mathrm{e}^x, xsin⁡xx\sin x and xln⁡xx\ln x.
What is q1?
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Find ∫e4x dx\displaystyle\int \mathrm{e}^{4x}\,dx. [2 marks]
What is q2?
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Find ∫xex dx\displaystyle\int x\mathrm{e}^x\,dx by parts. [3 marks]
What is q3?
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Find ∫3x2x3+2 dx\displaystyle\int \dfrac{3x^2}{x^3 + 2}\,dx. [2 marks]

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