Practice question · Put in order
Order the steps of integration by substitution for an indefinite integral.
- Spot an inner function whose derivative also appears in the integrand
- Integrate the resulting simpler integral in u
- Set u equal to that inner function
- Differentiate to get du = g'(x) dx and rewrite every x-part in terms of u
- Substitute u = g(x) back so the answer is a function of x
Hints
- Nothing can be rewritten until u has been chosen.
- Converting back is the last act, and only for an indefinite integral.
Show the answer
- Spot an inner function whose derivative also appears in the integrand
- Set u equal to that inner function
- Differentiate to get du = g'(x) dx and rewrite every x-part in terms of u
- Integrate the resulting simpler integral in u
- Substitute u = g(x) back so the answer is a function of x
Why
The order matters because the conversion of dx into du is what makes the method valid, not a formality. For a definite integral you may replace the final step by converting the limits instead.
Practise Integration by Substitution
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