X2-x2-a2x2-b2-k -a2-x2-a2-b2-x2-b2- k-

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Integration by Partial Fractions

x2/x2+a2x2+b2...

Question

$\frac{x^{2}}{(x^{2} + a^{2}) (x^{2} + b^{2})} = k [\frac{a^{2}}{x^{2} + a^{2}} - \frac{b^{2}}{x^{2} + b^{2}}] \Rightarrow k =$

1

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\frac{1}{a^{2} + b^{2}}

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\frac{1}{a^{2} - b^{2}}

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\frac{1}{b^{2} - a^{2}}

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Solution

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\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - \frac{z^{2}}{c^{2}} = 1, \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1, - \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1

x = \frac{\sqrt{a^{2} + b^{2}} + \sqrt{a^{2} - b^{2}}}{\sqrt{a^{2} + b^{2}} - \sqrt{a^{2} - b^{2}}}

b^{2} = \frac{2 a^{2} x}{x^{2} + 1}

x = \frac{\sqrt{a^{2} + b^{2}} + \sqrt{a^{2} - b^{2}}}{\sqrt{a^{2} + b^{2}} - \sqrt{a^{2} - b^{2}}}

a^{2} - b^{2} = \frac{2 a^{2}}{x^{2} + 1}

x = \frac{\sqrt{a^{2} + b^{2}} + \sqrt{a^{2} - b^{2}}}{\sqrt{a^{2} + b^{2}} - \sqrt{a^{2} - b^{2}}}

b^{2} = \frac{2 a^{2} x}{x^{2} + 1}

\frac{x^{2}}{a^{2} + b^{2}} + \frac{y^{2}}{b^{2}} = 1, \frac{x^{2}}{a^{2}} + \frac{y^{2}}{a^{2} + b^{2}} = 1

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