can
be done by making the substitution
For
example to find
sub
and
so
the integral becomes
(1)
A Level Maths Notes: C4 – Integrating Quotients of Algebraic Expressions
Integrating any quotient of
the formcan
be done by making the substitutionFor
example to findsubandso
the integral becomes(1)
There is however an alternative method which is also useful for integrating quotients of higher order polynomials. Carry out long division first on the quotient and integrate the result.
For the example above,
and
the integral becomes
This is equivalent to (1) since C is arbitrary.
Example: Find
so
the integral becomes
Example: Find
so
the integral becomes
