Solveeit Logo

Question

Question: **.** \(\int_{0}^{\infty}\frac{x^{2}dx}{(x^{2} + a^{2})(x^{2} + b^{2})(x^{2} + c^{2})}\) =\(\frac{\p...

. 0x2dx(x2+a2)(x2+b2)(x2+c2)\int_{0}^{\infty}\frac{x^{2}dx}{(x^{2} + a^{2})(x^{2} + b^{2})(x^{2} + c^{2})} =π2(a+b)(b+c)(c+a)\frac{\pi}{2(a + b)(b + c)(c + a)}

then0dx(x2+4)(x2+9)\int_{0}^{\infty}\frac{dx}{(x^{2} + 4)(x^{2} + 9)} =

A

π60\frac{\mathbf{\pi}}{\mathbf{60}}

B

π20\frac{\mathbf{\pi}}{\mathbf{20}}

C

π40\frac{\mathbf{\pi}}{\mathbf{40}}

D

π80\frac{\mathbf{\pi}}{\mathbf{80}}

Answer

π60\frac{\mathbf{\pi}}{\mathbf{60}}

Explanation

Solution

put c = 0, a = 2, b = 3