Ali's Improper Integrals: Problem 1

Calculus Level 3

If aa and bb are positive coprime integers in the following integral:

02x21x4+5x2+4dx=aπb,\int_0^\infty \frac{2x^2-1}{x^4+5x^2+4}dx=\frac{a\pi}{b},

find the value of a+ba+b.

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