Answer
$$\int_{1}^{\infty} \int_{1}^{\infty} \frac{1}{x y} d x d y=\infty$$
Work Step by Step
$$\int_{1}^{\infty} \int_{1}^{\infty} \frac{1}{x y} d x d y$$
So, we get
\begin{align}
\int_{1}^{\infty} \int_{1}^{\infty} \frac{1}{x y} d x d y
&=\int_{1}^{\infty}\frac{1}{ y} \left(\int_{1}^{\infty} \frac{1}{x} d x \right)d y\\
&=\int_{1}^{\infty}\left[\frac{1}{y} \ln x\right]_{1}^{\infty} d y\\
&=\int_{1}^{\infty}\left[\frac{1}{y}(\ln\infty)-\frac{1}{y}(\ln1)\right] d y\\
&=\int_{1}^{\infty}\left[\frac{1}{y}(\infty)-\frac{1}{y}(0)\right] d y\\
&=\infty
\end{align}
Because the integral diverges, the solution is infinity.
