A-level · Integration

Integration by reversing the chain ruleExam-style questions

Integrating by recognition — spotting the chain rule's fingerprint, the derivative of an inside function sitting as a factor. A power of a function; adjusting the answer when the factor is a number out; the log case, when the top is the derivative of the bottom; exponential and trig insides; and how to tell when recognition fails and you need to expand or substitute.

Start practising Read the lesson

19 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    Find ∫2x(x2+1)3 dx\displaystyle\int 2x(x^2 + 1)^3\,dx.
    Level 2 · 2 marksTry it
  2. 2
    Find ∫6x2x3+4 dx\displaystyle\int \frac{6x^2}{x^3 + 4}\,dx.
    Level 2 · 2 marksTry it
  3. 3
    Find ∫3x2(x3−2)5 dx\displaystyle\int 3x^{2}(x^{3} - 2)^{5}\,dx. (3 marks)
    Level 2 · 3 marksTry it