A-level · Integration

Integration by substitutionExam-style questions

Integrating by changing the variable — for integrals recognition cannot do. Choosing u to rename the awkward part; replacing dx with du; making every x disappear, including the strays; integrating in u and converting back; changing the limits of a definite integral so nothing converts back; and choosing a substitution, including a root or a trig function.

Start practising Read the lesson

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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
Using the substitution $u = x^2 - 3$ , find $\displaystyle\int x(x^2 - 3)^4\,dx$ .
Level 2 · 3 marksTry it