A charged rod of length $L$ produces an electric field at point $P(a,b)$ given by $$E(P)=\int_{-a}^{\,L-a} {\frac{c\,b}{4\pi p(x^2+b^2)^{3/2}}}\,dx$$ where $c$ is the charge density per unit length on the rod and $p$ is the free space permittivity (see the figure). Evaluate the integral to determine an expression for the electric field $E(P).$

$E(P) =$