## Calculus (3rd Edition)

We have $\int_{-\infty}^{\infty} \dfrac{ x dx}{1+x^2} \ dx=\lim\limits_{R \to \infty} \int_{-\infty}^0\dfrac{ x dx}{1+x^2} \ dx \\=\lim\limits_{R \to \infty} \dfrac{1}{2} \ln (R^2+1) \\=\infty$ Also, $\int_0^\infty \dfrac{x dx}{1+x^2}=\lim\limits_{R \to \infty} \int_0^{R} \dfrac{x dx}{1+x^2}\\=\lim\limits_{R \to \infty} \dfrac{1}{2} \ln (R^2+1) \\=\infty$ Hence, the integral diverges.