Partial Fractions...

[RESmonkey]

I'm not sure, but I'm looking over my notes and it seems my teacher may have made a mistake...

Use partial fractions to break this thing down into something that's easier to integrate:

(x^2)/((X^2)+2x+1)

First, he divided it out into:

1-(-2x-1)/((x^2)+2x+1)
=
1-(2x+1)/((x^2)+2x+1)


Then he started the partial fractioning of the latter part of ^^^^^

(2x+1)/((x^2)+2x+1)

=

(2x+1)/((x+1)^2)

=

A/(x+1) + B/((x+1)^2) ***this part

He got A =2 and B = -1.

BUT, I think he should have done THIS instead:

A/(x+1) + (Bx+C)/((x+1)^2)

This is because on a similar problem with a (*x + constant) as a numerator, he pulled a (Bx + C) instead of a B.


Thanks much

 

[esun]

Take a look at the examples here, they will clarify things a lot: http://en.wikipedia.org/wiki/Partial_fractions

In particular, look at the section entitled "Repeated factors in the denominator generally". In short, he's right.

 

[RESmonkey]

You're right. Shame on me...