Integrating Quotients of Algebraic Expressions

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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

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