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Cambridge AS & A Level Mathematics

3.5bIntegration by recognition and by substitution

Integration by recognition and by substitution in Cambridge AS & A Level Mathematics: what the syllabus expects you to know, the learning objectives and how to practise.
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Learning objectives

What the syllabus expects you to be able to do.

  1. 3.5.4Paper 3: recognise an integrand of the form k f′(x)/f(x) and integrate it.
  2. 3.5.6Paper 3: use a given substitution to simplify and evaluate a definite or indefinite integral.

Lessons

  • Integration by recognition and by substitution

    45 min

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Sample question

A sample question on this topic. Answer it, check it, then read the worked answer.

Integration by recognition and by substitution: sample question

1 mark

Find ∫2xx2+5 dx\displaystyle\int\frac{2x}{x^{2} + 5}\,dx. Type ln for the natural logarithm and include the constant, for example ln(x^2+1)+c.

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