renegade05
Full Member
- Joined
- Sep 10, 2010
- Messages
- 260
I am studying for my CALC II final and just brushing up on my integration using the partial fractions technique.
I remember learning this topic and something that i never understood was the repeated linear factors. My text and teacher never showed how this works, just how to do it. I HATE WHEN THEY DO THIS.
Anyway, here is my confusion:
Say you have:
\(\displaystyle \[ \int \frac{x}{(x+3)^2}\,dx\]\)
I know to solve this you must set it up like this:
\(\displaystyle \int\frac{x}{(x+3)^2}\,dx=\)\(\displaystyle \int \frac{A}{(x+3)}+\frac{B}{(x+3)^2}\,dx\)
I just wanna know why do we split it like this? Why does the A term get an \(\displaystyle (x+3)\) and the B term gets an \(\displaystyle (x+3)^2\) ? I mean i can do it no problem just due to memorizing the technique, but i would just like to know how this works.
Am I just reading into this too much ? Am I missing something easy here?
Thanks!
I remember learning this topic and something that i never understood was the repeated linear factors. My text and teacher never showed how this works, just how to do it. I HATE WHEN THEY DO THIS.
Anyway, here is my confusion:
Say you have:
\(\displaystyle \[ \int \frac{x}{(x+3)^2}\,dx\]\)
I know to solve this you must set it up like this:
\(\displaystyle \int\frac{x}{(x+3)^2}\,dx=\)\(\displaystyle \int \frac{A}{(x+3)}+\frac{B}{(x+3)^2}\,dx\)
I just wanna know why do we split it like this? Why does the A term get an \(\displaystyle (x+3)\) and the B term gets an \(\displaystyle (x+3)^2\) ? I mean i can do it no problem just due to memorizing the technique, but i would just like to know how this works.
Am I just reading into this too much ? Am I missing something easy here?
Thanks!