Math — Partial Fractions

\frac{1}{(x-a)(x-b)} = \frac{A}{x-a} + \frac{B}{x-b}

\frac{px+q}{(x-a)^2} = \frac{A}{x-a} + \frac{B}{(x-a)^2}

\int \frac{dx}{x^2 - a^2} = \frac{1}{2a}\ln\left|\frac{x-a}{x+a}\right| + C

\int \frac{dx}{x^2 + a^2} = \frac{1}{a}\arctan\frac{x}{a} + C