1. a) Express (x+3)/x²(x-1) in terms of partial fractions
b) Find ∫(x+3)/x²(x-1)dx
Not sure if i need to expand the denominator in a?
really have no idea how to do b!
$\displaystyle
\frac{x+3}{x^2(x-1)} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x-1}
$
$\displaystyle x+3 = Ax(x-1) + B(x-1) + Cx^2$
let $\displaystyle x = 1$ ... $\displaystyle C = 4$
let $\displaystyle x = 0$ ... $\displaystyle B = -3$
let $\displaystyle x = 2$ ... $\displaystyle A = -4$
$\displaystyle \int \frac{x+3}{x^2(x-1)} \, dx = \int -\frac{4}{x} - \frac{3}{x^2} + \frac{4}{x-1} \, dx
$