Ali's Improper Integrals: Problem 1

Calculus Level 4

If \(a\) and \(b\) are positive coprime integers in the following integral:

\[\int_0^\infty \frac{2x^2-1}{x^4+5x^2+4}dx=\frac{a\pi}{b},\]

find the value of \(a+b\).

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