Question

Partial fraction Integration?
Integrate: (1-v^2)/(v+v^3)

Answer 1

\[\frac{1-v^2}{v+v^3}=\frac{1-v^2}{v(1+v^2)}=\frac{A}{v}+\frac{Bv+C}{1+v^2}\]

Answer 2

book says to factor denominator v(1+v^2) and use the parts as the denominator for A+B

(1-v^2)/(v+v^3) = A/v + B/1+v^2 and then multiply bot sides which should cancel most things out

1-v^2 = A(1+v^2) + Bv then multiply out

1-v^2 = A + Av^2 + Bv then dunno

Answer 3

\[1-v^2=A+Av^2+Bv^2+Cv\]
Giving the system
\[\begin{cases}A+B=-1\\C=0\\A=1\end{cases}\]

Answer 4

I'm using "how to ace calculus" for my instructions they didn't have the c part...

I got the A=1 when I set v = 0.... aaak I have A+B=1 but that was me losing the sign...

Answer 5

Right, well that setup isn't correct. You have a quadratic factor in the denominator, so you must use a linear factor in the numerator.

Answer 6

ok so v^3 means I need three fractions?

Answer 7

so B=-2 and plug that back into the A/v + (Bv+c)/1+v^2

Answer 8

Wait, I'm not sure what you're asking. We don't end up using three fractions here because we can't break up the quadratic factor any further.

Answer 9

But yeah, you find A and B and integrate one fraction at a time.

Answer 10

I think I got it ...gonna take more practice...thanks

Answer 11

yw