Evaluate ∫−∞∞1(x2+a2)(x2+b2)dx\int_{-\infty}^{\infty} \frac{1}{(x^2+a^2)(x^2+b^2)} dx∫−∞∞(x2+a2)(x2+b2)1dx for a,b>0,a≠ba, b > 0, a \neq ba,b>0,a=b.
πab(a+b)\frac{\pi}{ab(a+b)}ab(a+b)π
πa+b\frac{\pi}{a+b}a+bπ
πa2−b2\frac{\pi}{a^2-b^2}a2−b2π
1a+b\frac{1}{a+b}a+b1