Solving System of Equations: Partial Fraction Decomposition Help

khatche4
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Hello. I'm trying to solve a system of equations problem (for my Partial Fraction Decomposition problem)...

1 = -4 + 2B + 2C + D + E
3 = 4 - 2B + 2C - D + E
3 = -25 + 20B + 10C + 4D + 2E
5 = 25 - 20B + 10C - 4D + 2E

So that boils down to..

1 = 2C + E
3 = 2C + E
3 = 10C + 2E
5 = 10C + 2E
right??

I tried substitution, but that didn't work. Elimination doesn't work, either... So what else? I'm pretty sure you can do it graphically, but I can't remember...

Help, please! I'm doing this last minute (I know I shouldn't be, but I desperately need help!)
 
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Something is not right here.

if you multiply your first equation by 5, you get: 5 = 10C + 5E

but your last equation is: 5 = 10C + 2E

So which is it? I think you may have made a mistake somewhere coming up with these equations.
 
What was the original "partial fractions" problem?
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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