# Thread: Integration by partical fractions

1. ## Integration by partical fractions

I have the following integral to evaluate and determine the values for A and B

x + 1 / (x + 2) (x - 3) so I would have

A/(x + 2) and B / (x-3) therefore

x + 1 = A(x-3) + B (x+2)

Equating the coefficients:
A + B = 1

-3A + 2B = 1

THe answer the sample test gives for A is 1/5 !!! I could understand this if it were 3A not -3A Can someone please tell me am I going crazy or did the teacher make a mistake in the orginal problem and it should read

2. $A + B = 1 \: \: \iff \: \: A = 1 - B$

Substitute:
$-3(1-B) + 2B = 1$
$-3 + 3B + 2B = 1$
$5B = 4$
$B = \frac{4}{5}$

Plug back into your first equation:
$A + \left(\frac{4}{5}\right) = 1$
$A = 1 - \frac{4}{5} = \frac{1}{5}$