Distinct Linear Factors
$$\int \frac{3x + 5}{(x+1)(x-2)} \, dx$$
Select the correct decomposition or antiderivative from the choices below:
Step-by-Step Breakdown:
Decomposition Rules
Distinct Linear Factors:
$\frac{P(x)}{(x-a)(x-b)} = \frac{A}{x-a} + \frac{B}{x-b}$
Repeated Linear Factors:
$\frac{P(x)}{(x-a)^2(x-b)} = \frac{A}{x-a} + \frac{B}{(x-a)^2} + \frac{C}{x-b}$
Irreducible Quadratic Factors:
$\frac{P(x)}{(x^2+a)(x-b)} = \frac{Ax+B}{x^2+a} + \frac{C}{x-b}$