# 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 $$\displaystyle \int_{0}^{\infty} {\dfrac{1}{( x^{2} + 4 ) ( x^{2} + 9 )}} \,dx$$