# Integrate It to Infinity

Calculus Level 5

$\large \int_0^\infty\dfrac{x^2 }{(x^2+a^2)(x^2+b^2)(x^2+c^2)} \, dx =\dfrac{\pi}{n}$

Let $$a,b$$ and $$c$$ be the real roots of the cubic equation $$x^3-7x^2+10x-2=0$$. Find the value of the positive integer $$n$$ that satisfy the equation above.

×