Partial Fraction - Application To Symbolic Integration

Application To Symbolic Integration

For the purpose of symbolic integration, the preceding result may be refined into

Let ƒ and g be nonzero polynomials over a field K. Write g as a product of powers of pairwise coprime polynomials which have no multiple root in an algebraically closed field:

There are (unique) polynomials b and c ij with deg c ij < deg p i such that
\frac{f}{g}=b+\sum_{i=1}^k\sum_{j=2}^{n_i}\left(\frac{c_{ij}}{p_i^{j-1}}\right)' + \sum_{i=1}^k \frac{c_{i1}}{p_i}.
where denotes the derivative of

This reduces the computation of the antiderivative of a rational function to the integration of the last sum, with is called the logarithmic part, because its antiderivative is a linear combination of logarithms.

Read more about this topic:  Partial Fraction

Famous quotes containing the words application to, application, symbolic and/or integration:

    “If you would be a favourite of your king, address yourself to his weaknesses. An application to his reason will seldom prove very successful.”
    —Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)

    “My business is stanching blood and feeding fainting men; my post the open field between the bullet and the hospital. I sometimes discuss the application of a compress or a wisp of hay under a broken limb, but not the bearing and merits of a political movement. I make gruel—not speeches; I write letters home for wounded soldiers, not political addresses.”
    —Clara Barton (1821–1912)

    “The symbolic view of things is a consequence of long absorption in images. Is sign language the real language of Paradise?”
    —Hugo Ball (1886–1927)

    “Look back, to slavery, to suffrage, to integration and one thing is clear. Fashions in bigotry come and go. The right thing lasts.”
    —Anna Quindlen (b. 1952)