Integration by Substitution (Edexcel A Level Maths): Revision Note
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Substitution (Reverse Chain Rule)
What is integration by substitution?
Make sure you are familiar with Chain Rule and Reverse Chain Rule
In more awkward problems it is harder to spot the reverse chain rule
It is possible to use a substitution
These kinds of substitutions usually will not be given
The substitution is deemed ‘obvious’
How do I integrate when a substitution is not given?
Look to substitute the ‘second’ (rather than the ‘main’) function
STEP 1: Determine the substitution
What is the ‘main’ function? ‘second’ function?
STEP 2: Differentiate the substitution and rearrange
du/dx here can be treated like a fraction (eg × dx to get rid of fractions)
STEP 3: Replace all parts of the integral
all x terms should be replaced with equivalent u terms, including dx
if a definite integral change the limits from x to u too
STEP 4: Integrate and either …
…substitute x back in
or
… evaluate the definite integral using the u limits
STEP 5: Find c, the constant of integration, if needed
Examiner Tips and Tricks
A lot of the “work” in these problems happens in your head :
what is the ‘main’ function?
what should the substitution be?
are there any numbers to ‘adjust’ and ‘compensate’ for?
Be sure that what you write down is clear and easy to follow, and remember that you can check your final answer by differentiating it.
Worked Example
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