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## Homework Statement

w=(PI*(P0-PL)*R^4*epsilon^3*row)/6*mu*L)*(1-1/2*epsilon)

show that this can be obtained using

w=(PI*(P0-PL)*R^4*row)/8*mu*L)*((1-kappa^4)-((1-kappa^2)^2/ln(1/kappa))

by setting kappa equal to 1-epsilon and expanding the expression for w in powers of epsilon. this requires using the Taylor series ln(1-epsilon)=-epsilon-1/2*epsilon^2-1/3*epsilon^3-...

## The Attempt at a Solution

so far I have plugged in 1-epsilon for all the kappas, expanded everything and canceled what I could and have ended up with this:

w=(PI*(P0-PL)*R^4*row)/8*mu*L)*epsilon*((-3*x^6+8*x^5-8*x^4+40*x^2-96*x+96)/(3*x^3+4*x^2+6*x+12))

I found an online polynomial long division calculator but I still end up with a jumbled mess. I was wondering if anyone had any ideas or did I make a mistake in the middle somewhere and that is why things aren't turning out nicely. Thanks so much.