1. Partial fractions

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!

2. Originally Posted by djmccabie
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!
$\displaystyle \frac{x+3}{x^2(x-1)}$

$\displaystyle = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x-1}$

3. Originally Posted by djmccabie
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! that's why you do (a) first
$\displaystyle \frac{x+3}{x^2(x-1)} = \frac{A}{x} + \frac{B}{x^2} + \frac{C}{x-1}$

$\displaystyle x+3 = Ax(x-1) + B(x-1) + Cx^2$

let $\displaystyle x = 1$ ... $\displaystyle C = 4$

let $\displaystyle x = 0$ ... $\displaystyle B = -3$

let $\displaystyle x = 2$ ... $\displaystyle A = -4$

$\displaystyle \int \frac{x+3}{x^2(x-1)} \, dx = \int -\frac{4}{x} - \frac{3}{x^2} + \frac{4}{x-1} \, dx$

4. hi just a question. When you let x=2, what happens to B and C ?

5. Replace them with the values you already had: B= -3, C= 4.