Answer
Convergent
Work Step by Step
Here, we have $\int_0^{\infty} \dfrac{10}{x^2+3^2}=\dfrac{10}{3} \lim\limits_{n \to \infty}[ \tan^{-1}(x/3)]$
or, $=\dfrac{10}{3} [ \tan^{-1}(\infty/3)-\tan^{-1}(0/3)]$
or, $=\dfrac{10}{3}[\dfrac{\pi}{2}-\dfrac{\pi}{2}]$
or, $=0$
So, we can see that the given series is convergent by the integral test.
