# Thread: Integration using partial fractions

1. ## Integration using partial fractions

Find , where

I know that you need to use partial fractions to integrate this but im having trouble finding the partial fractions. Could someone point me in the right direction? Cheers.

2. Originally Posted by Haris
Find , where

I know that you need to use partial fractions to integrate this but im having trouble finding the partial fractions. Could someone point me in the right direction? Cheers.
Factorise the denominator to :

$(y+6)(y-3)$

So you have:

$\frac{4y-10}{(y+6)(y-3)} = \frac{A}{y+6} + \frac{B}{y-3}$

Now multiply through by $(y+6)(y-3)$

$4y-10 = A(y-3)+ B(y+6)$

$4y-10 = Ay-3A+ By+6B$

Now compare coefficients of $y$ and $1$:

$4y = Ay + By$

$\therefore A+B = 4$

$-10 = -3A + 6B$

Solve by simultaneous equations!