Let's do some calculus! (24)

Calculus Level 3

\[\large \displaystyle \int_{0}^{\infty} {\dfrac{x^{2}}{( x^{2} + a^{2} )( x^{2} + b^{2} )( x^{2} + c^{2} )}} \,dx = \dfrac{\pi}{2 ( a+b )( b+c )( c+a )}\]

Given that the equation above holds true for constant reals \(a\), \(b\) and \(c\), find the value of \(\displaystyle \int_{0}^{\infty} {\dfrac{1}{( x^{2} + 4 ) ( x^{2} + 9 )}} \,dx\)


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