If ∫(x^2/(x^2 + a^2)(x^2 + b^2)(x^2 + c^2)) dx for x ∈ [0,∞] = π/2(a + b)(b + c)(c + a), find the value of ∫(dx/(x^2 +

If ∫(x²/(x² + a²)(x² + b²)(x² + c²)) dx for x ∈ [0,∞] = π/2(a + b)(b + c)(c + a), find the value of ∫(dx/(x² + 4)(x² + 9)) for x ∈ [0,∞].

If ∫(x^2/(x^2 + a^2)(x^2 + b^2)(x^2 + c^2)) dx for x ∈ [0,∞] = π/2(a + b)(b + c)(c + a), find the value of ∫(dx/(x^2 + 4)(x^2 + 9))