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If aaa and bbb are positive coprime integers in the following integral:
∫0∞2x2−1x4+5x2+4dx=aπb,\int_0^\infty \frac{2x^2-1}{x^4+5x^2+4}dx=\frac{a\pi}{b},∫0∞x4+5x2+42x2−1dx=baπ,
find the value of a+ba+ba+b.
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