Partial Fractions In Integration
In integral calculus, partial fraction expansions provide an approach to integrating a general rational function. Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of algebraic fractions. Each fraction in the expansion has as its denominator a polynomial function of degree 1 or 2, or some positive integer power of such a polynomial. (In the case of rational function of a complex variable, all denominators will have a polynomial of degree 1, or some positive integer power of such a polynomial.) If the denominator is a 1st-degree polynomial or a power of such a polynomial, then the numerator is a constant. If the denominator is a 2nd-degree polynomial or a power of such a polynomial, then the numerator is a 1st-degree polynomial.
Isaac Barrow's proof of the integral of the secant function was the earliest use of partial fractions in integration. In 1599, Edward Wright gave a solution by numerical methods – what today we would call Riemann sums.
Read more about Partial Fractions In Integration: A 1st-degree Polynomial in The Denominator, A Repeated 1st-degree Polynomial in The Denominator, An Irreducible 2nd-degree Polynomial in The Denominator, A Repeated Irreducible 2nd-degree Polynomial in The Denominator
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