\(\int_{V_{\infty}}^{V_{x}} d V=-\int_{\infty}^{x} \vec{E}_{G} \cdot \vec{d}_{x}\)

\(V _{ x }- V _{\infty}=-\int_{\infty}^{ x } \frac{ Ax }{\left( x ^{2}+ a ^{2}\right)^{3 / 2}} d x\)

put \(x^{2}+a^{2}=z\)

\(2 x dx = dz\)

\(V_{x}-0=-\int_{\infty}^{x} \frac{A d z}{2(z)^{3 / 2}}=\left[\frac{A}{z^{1 / 2}}\right]_{\infty}^{x}=\left[\frac{A}{\left(x^{2}+a^{2}\right)^{1 / 2}}\right]_{\infty}^{x}\)

\(V_{x}=\frac{A}{\left(x^{2}+a^{2}\right)^{1 / 2}}-0=\frac{A}{\left(x^{2}+a^{2}\right)^{1 / 2}}\)