7.4 Integration by Partial Fraction Decomposition Review

The quotient of polynomials P (x)/Q(x) can be decomposed into a sum of partial fractions provided that:

the degree of the numerator polynomial P (x) is strictly smaller than the degree of the denominator polynomial Q(x).

If the partial fraction has denominator of a linear function or a product of linear functions then

the numerator is a constant

If the partial fraction has a denominator of quadratics that cannot be factored further then

the numerator is a linear expression

denominator : degree n

numerator: degree n-1

int(1/(ax+b) dx)

(1/a)(log|ax+b|) + C

int(1/(x²+a²) dx)

(1/a)arctan(x/a) + C

int((bx + c) / (x² + a²) dx)

int(bx / (x² + a²) dx) + int(c / (x² + a²) dx)