12. Techniques of Integration

Express the rational function as a sum or difference of two simpler fractions. Use a system of equations.

$\frac{1}{(2x+1)(2x-1)}$

Express the rational function as a sum or difference of two simpler fractions. Use a system of equations.

$\frac{4x^2-21x-40}{x^3-x^2-20x}$

Give the partial fraction decomposition for the following expression using strategic substitutions for $x$.

$\frac{4x^2-8x-8}{x(x-2)(x+2)}$

Express the rational function as a sum or difference or simpler rational expressions.

$\frac{4}{x^3-3x^2-x+3}$